Dr Mike Hirschhorn

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Phone

9385 7093

E-mail

m.hirschhorn@unsw.edu.au

Location

School of Mathematics and Statistics UNSW Sydney NSW 2052 The Red Centre Room 6109

Publications

Books | 2017

Hirschhorn MD, 2017, Erratum to: The Power of q Developments in Mathematics 49, 10.1007/978-3-319-57762-3, http://dx.doi.org/10.1007/978-3-319-57762-3_44

Books | 2017

Hirschhorn MD, 2017, The Power of q A Personal Journey, Springer
Book Chapters | 2021

Chern S; Hirschhorn MD, 2021, 'Partitions into Distinct Parts Modulo Powers of 5', in George E. Andrews 80 Years of Combinatory Analysis, pp. 305 - 328, http://dx.doi.org/10.1007/978-3-030-57050-7_17

Book Chapters | 2017

Hirschhorn MD, 2017, 'Introduction', in Developments in Mathematics, pp. 1 - 17, http://dx.doi.org/10.1007/978-3-319-57762-3_1
Journal articles | 2022

da Silva R; Hirschhorn MD; Sellers JA, 2022, 'Elementary proofs of infinitely many congruences for k-elongated partition diamonds', Discrete Mathematics, 345, http://dx.doi.org/10.1016/j.disc.2022.113021

Journal articles | 2021

Chern S; Hirschhorn MD, 2021, 'Some results concerning partitions with designated summands', Ramanujan Journal, 54, pp. 385 - 395, http://dx.doi.org/10.1007/s11139-019-00198-1

Journal articles | 2020

Hirschhorn MD; Sellers JA, 2020, 'Congruences for overpartitions with restricted odd differences', Ramanujan Journal, 53, pp. 167 - 180, http://dx.doi.org/10.1007/s11139-019-00156-x

Journal articles | 2020

Hirschhorn MD, 2020, 'Cubic partitions modulo powers of 5', Ramanujan Journal, 51, pp. 67 - 84, http://dx.doi.org/10.1007/s11139-018-0074-z

Journal articles | 2019

Chern S; Hirschhorn MD, 2019, 'Partitions into Distinct Parts Modulo Powers of 5', Annals of Combinatorics, 23, pp. 659 - 682, http://dx.doi.org/10.1007/s00026-019-00439-6

Journal articles | 2019

Hirschhorn MD; Sellers JA, 2019, 'PARITY RESULTS for PARTITIONS WHEREIN EACH PART APPEARS AN ODD NUMBER of TIMES', Bulletin of the Australian Mathematical Society, 99, pp. 51 - 55, http://dx.doi.org/10.1017/S0004972718001041

Journal articles | 2019

Hirschhorn MD, 2019, 'Two remarkable q-series expansions', Ramanujan Journal, 49, pp. 451 - 463, http://dx.doi.org/10.1007/s11139-018-0016-9

Journal articles | 2018

Hirschhorn MD, 2018, 'A conjecture of B. Lin on cubic partition pairs', Ramanujan Journal, 45, pp. 781 - 795, http://dx.doi.org/10.1007/s11139-017-9926-1

Journal articles | 2018

Hirschhorn MD, 2018, 'Broken 2-diamond partitions modulo 5', Ramanujan Journal, 45, pp. 517 - 520, http://dx.doi.org/10.1007/s11139-016-9863-4

Journal articles | 2018

Hirschhorn MD, 2018, 'Congruences modulo 5 for partitions into at most four parts', Fibonacci Quarterly, 56, pp. 32 - 37, http://dx.doi.org/10.1080/00150517.2018.12427718

Journal articles | 2018

Hirschhorn MD, 2018, 'Partitions in 3 colours', Ramanujan Journal, 45, pp. 399 - 411, http://dx.doi.org/10.1007/s11139-016-9835-8

Journal articles | 2017

Gireesh DS; Hirschhorn MD; Naika MSM, 2017, 'On 3-regular partitions with odd parts distinct', Ramanujan Journal, 44, pp. 227 - 236, http://dx.doi.org/10.1007/s11139-016-9814-0

Journal articles | 2017

Hirschhorn MD, 2017, 'Partitions and powers of 13', Journal of Number Theory, 178, pp. 146 - 157, http://dx.doi.org/10.1016/j.jnt.2017.02.016

Journal articles | 2016

Hirschhorn MD; Sellers JA, 2016, 'Infinitely many congruences modulo 5 for 4-colored Frobenius partitions', Ramanujan Journal, 40, pp. 193 - 200, http://dx.doi.org/10.1007/s11139-014-9652-x

Journal articles | 2016

Hirschhorn MD, 2016, 'On the 2- and 4-dissections of the Rogers–Ramanujan functions', Ramanujan Journal, 40, pp. 227 - 235, http://dx.doi.org/10.1007/s11139-014-9657-5

Journal articles | 2016

Hirschhorn MD, 2016, 'Some congruences for 6-colored generalized Frobenius partitions', Ramanujan Journal, 40, pp. 463 - 471, http://dx.doi.org/10.1007/s11139-015-9700-1

Journal articles | 2015

Chen SC; Hirschhorn MD; Sellers JA, 2015, 'Arithmetic properties of Andrews' singular overpartitions', International Journal of Number Theory, 11, pp. 1463 - 1476, http://dx.doi.org/10.1142/S1793042115400011

Journal articles | 2015

Eichhorn DA; Hirschhorn MD, 2015, 'Notes on the spt function of George E. Andrews', Ramanujan Journal, 38, pp. 17 - 34, http://dx.doi.org/10.1007/s11139-013-9554-3

Journal articles | 2015

Hirschhorn MD; Toh PC, 2015, 'On a certain vector crank modulo 7', Electronic Journal of Combinatorics, 22, http://dx.doi.org/10.37236/4316

Journal articles | 2015

Hirschhorn MD, 2015, 'A connection between π and Φ', The Fibonacci Quarterly, 53, pp. 42 - 47, http://www.fq.math.ca/53-1.html

Journal articles | 2015

Hirschhorn MD, 2015, 'Binomial identities and congruences for Euler numbers', Fibonacci Quarterly, 53, pp. 319 - 322, http://dx.doi.org/10.1080/00150517.2015.12428250

Journal articles | 2015

Hirschhorn MD, 2015, 'Elementary analysis in Ramanujan’s lost notebook', Ramanujan Journal, 37, pp. 641 - 651, http://dx.doi.org/10.1007/s11139-013-9551-6

Journal articles | 2015

Hirschhorn MD, 2015, 'Ramanujan’s Last Problem', The Fibonacci Quarterly, 53, pp. 48 - 52

Journal articles | 2015

Hirschhorn MD, 2015, 'Some interesting q-series identities', Ramanujan Journal, 36, pp. 297 - 304, http://dx.doi.org/10.1007/s11139-014-9646-8

Journal articles | 2014

Hirschhorn MD; Sellers JA, 2014, 'A congruence modulo 3 for partitions into distinct non-multiples of four', Journal of Integer Sequences, 17

Journal articles | 2014

Hirschhorn MD; Sellers JA, 2014, 'Arithmetic properties of 1-shell totally symmetric plane partitions', Bulletin of the Australian Mathematical Society, 89, pp. 473 - 478

Journal articles | 2014

Hirschhorn MD; Villarino MB, 2014, 'A refinement of Ramanujan's factorial approximation', Ramanujan Journal, 34, pp. 73 - 81, http://dx.doi.org/10.1007/s11139-013-9494-y

Journal articles | 2014

Hirschhorn MD, 2014, 'A short and simple proof of Ramanujan's mod 11 partition congruence', Journal of Number Theory, 139, pp. 205 - 209, http://dx.doi.org/10.1016/j.jnt.2013.12.014

Journal articles | 2014

Hirschhorn MD, 2014, 'Stirling without Wallis', Fibonacci Quarterly, 52, pp. 321 - 324, http://dx.doi.org/10.1080/00150517.2014.12427879

Journal articles | 2014

Hirschhorn MD, 2014, 'The number of different parts in the partitions of n', Fibonacci Quarterly, 52, pp. 10 - 15, http://dx.doi.org/10.1080/00150517.2014.12427914

Journal articles | 2013

Hirschhorn MD; Sinescu V, 2013, 'Elementary Algebra in Ramanujan’s Lost Notebook', Fibonacci Quarterly, 51, pp. 123 - 129, http://web.maths.unsw.edu.au/~mikeh/webpapers/paper187.pdf

Journal articles | 2013

Hirschhorn MD; Villarino MB, 2013, 'A naive proof that F5n ≡ 0 (mod 5)', Fibonacci Quarterly, 51, pp. 256 - 258

Journal articles | 2013

Hirschhorn MD, 2013, 'A NAIVE PROOF THAT F-5n equivalent to 0 (mod 5)', FIBONACCI QUARTERLY, 51, pp. 256 - 258, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000217590800008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 2013

Hirschhorn MD, 2013, 'A constant in a formula of Ramanujan', Mathematical Gazette, 97, pp. 276, http://dx.doi.org/10.1017/S0025557200005921

Journal articles | 2013

Hirschhorn MD, 2013, 'A sequence considered by Shaun Cooper', New Zealand Journal of Mathematics (Online), 43, pp. 31 - 36, http://web.maths.unsw.edu.au/~mikeh/webpapers/paper183.pdf

Journal articles | 2013

Hirschhorn MD, 2013, 'Estimating the apery numbers II', Fibonacci Quarterly, 51, pp. 215 - 217, http://dx.doi.org/10.1080/00150517.2013.12427939

Journal articles | 2013

Hirschhorn MD, 2013, 'Factorizations of certain q-series identities of Ramanujan and others', Ramanujan Journal, 31, pp. 15 - 22, http://dx.doi.org/10.1007/s11139-012-9419-1

Journal articles | 2013

Hirschhorn MD, 2013, 'THE ASYMPTOTIC BEHAVIOR OF Pi(n)(k=0) (n k)', FIBONACCI QUARTERLY, 51, pp. 163 - 173, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000217589800011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 2013

Hirschhorn MD, 2013, 'The asymptotic behavior of \prod_{k=1}^n\binom{n,k}', Fibonacci Quarterly, 51, pp. 163 - 173

Journal articles | 2013

Hirschhorn MD, 2013, 'The number of 1's in the partitions of n', Fibonacci Quarterly, 51, pp. 326 - 329, http://dx.doi.org/10.1080/00150517.2013.12427931

Journal articles | 2012

Hirschhorn MD, 2012, 'A note on overcubic partitions', New Zealand Journal of Mathematics (Online), 42, pp. 229 - 234, http://web.maths.unsw.edu.au/~mikeh/webpapers/paper181.pdf

Journal articles | 2012

Hirschhorn MD, 2012, 'Estimating the Apery numbers', Fibonacci Quarterly, 50, pp. 129 - 131

Journal articles | 2012

Hirschhorn MD, 2012, 'Inequalities for Euler's constant', Mathematical Gazette, 96, pp. 133 - 136, http://dx.doi.org/10.1017/S0025557200004174

Journal articles | 2012

Hirschhorn MD, 2012, 'Ramanujan's enigmatic formula for the harmonic series', Ramanujan Journal, 27, pp. 343 - 347, http://dx.doi.org/10.1007/s11139-011-9322-1

Journal articles | 2012

Hirschhorn MD, 2012, 'The number of sequences of n tosses of a coin with k pairs of consecutive heads', Fibonacci Quarterly, 50, pp. 140 - 143

Journal articles | 2012

Hirschhorn MD, 2012, '“Algebraical oddities” in Ramanujan’s lost notebook', Ramanujan Journal, 29, pp. 69 - 77, http://dx.doi.org/10.1007/s11139-012-9395-5

Journal articles | 2011

Cooper S; Hirschhorn MD, 2011, 'Factorizations that involve Ramanujan’s function k(q) = r(q)r 2(q 2)', ACTA Mathematica Sinica - English Series, 27, pp. 2301 - 2318, http://dx.doi.org/10.1007/s10114-011-0202-9

Journal articles | 2011

Hirschhorn M, 2011, '95.35 A surprising appearance of zeta(3)', MATHEMATICAL GAZETTE, 95, pp. 313 - 313, http://dx.doi.org/10.1017/S0025557200003120

Journal articles | 2011

Hirschhorn M, 2011, '95.40 Lord Brouncker's continued fraction for pi', MATHEMATICAL GAZETTE, 95, pp. 322 - 326, http://dx.doi.org/10.1017/S002555720000317X

Journal articles | 2011

Hirschhorn MD, 2011, 'A Simple Proof that ζ(2) = π²/6', Mathematical Intelligencer, 33, pp. 81 - 82, http://dx.doi.org/10.1007/s00283-011-9217-4

Journal articles | 2011

Hirschhorn MD, 2011, 'A note on Somos' quadratic recurrence constant', Journal of Number Theory, 131, pp. 2061 - 2063

Journal articles | 2011

Hirschhorn MD, 2011, 'A simple proof that zeta(2) = pi2/6', Mathematical Intelligencer, 33, pp. 81 - 82, http://dx.doi.org/10.1007/s00283-011-9217-4

Journal articles | 2011

Hirschhorn MD, 2011, 'A triangle-folding problem', MATHEMATICAL GAZETTE, 95, pp. 514 - 517, http://dx.doi.org/10.1017/S002555720000365X

Journal articles | 2011

Hirschhorn MD, 2011, 'An interesting integral', MATHEMATICAL GAZETTE, 95, pp. 90 - 91, http://dx.doi.org/10.1017/S0025557200002436

Journal articles | 2011

Hirschhorn MD, 2011, 'Approximating Euler's constant', Fibonacci Quarterly, 49, pp. 243 - 248

Journal articles | 2011

Hirschhorn MD, 2011, 'Commensurable triangles', MATHEMATICAL GAZETTE, 95, pp. 61 - 63, http://dx.doi.org/10.1017/S0025557200002345

Journal articles | 2011

Hirschhorn MD, 2011, 'Factorization of lens sequences', Fibonacci Quarterly, 49, pp. 110 - 115, http://dx.doi.org/10.1007/s11139-010-9272-z

Journal articles | 2011

Hirschhorn MD, 2011, 'Maximisation/minimisation without calculus', MATHEMATICAL GAZETTE, 95, pp. 83 - 85, http://dx.doi.org/10.1017/S0025557200002400

Journal articles | 2011

Hirschhorn MD, 2011, 'On the 2- and 4-dissections of Ramanujan's continued fraction and its reciprocal', Ramanujan Journal, 24, pp. 85 - 92, http://dx.doi.org/10.1007/s11139-010-9272-z

Journal articles | 2011

Hirschhorn MD, 2011, 'Ramanujan's "most beautiful identity"', American Mathematical Monthly, 118, pp. 839 - 845, http://dx.doi.org/10.4169/amer.math.monthly.118.09.839

Journal articles | 2011

Hirschhorn MD, 2011, 'Tenth order algorithms for calculating root 2, (sic)', MATHEMATICAL GAZETTE, 95, pp. 526 - 528, http://dx.doi.org/10.1017/S0025557200003697

Journal articles | 2011

Hirschhorn MD, 2011, 'When is the sum of consecutive squares a square?', MATHEMATICAL GAZETTE, 95, pp. 511 - 512, http://dx.doi.org/10.1017/S0025557200003636

Journal articles | 2010

Andrews GE; Hirschhorn MD; Sellers JA, 2010, 'Arithmetic properties of partitions with even parts distinct', Ramanujan Journal, 23, pp. 169 - 181, http://dx.doi.org/10.1007/s11139-009-9158-0

Journal articles | 2010

Hirschhorn MD; Sellers JA, 2010, 'Arithmetic properties of partitions with odd parts distinct', Ramanujan Journal, 22, pp. 273 - 284

Journal articles | 2010

Hirschhorn MD; Sellers JA, 2010, 'Elementary proofs of parity results for 5–regular partitions', Bulletin of the Australian Mathematical Society, 81, pp. 58 - 63

Journal articles | 2009

Hirschhorn MD; Rodseth OJ; Sellers JA, 2009, 'Infinite families of divisibility properties modulo 4 for non-squashing partitions into district parts', Integers, 9, pp. 427 - 433

Journal articles | 2009

Hirschhorn MD; Sellers JA, 2009, 'Elementary proofs of various facts about 3-cores', Bulletin of the Australian Mathematical Society, 79, pp. 507 - 512

Journal articles | 2009

Hirschhorn MD, 2009, 'A problem involving binomial coefficients', Australian Mathematical Society Gazette, 36, pp. 273 - 275

Journal articles | 2009

Hirschhorn MD, 2009, 'Comment on 'Counting paths in a grid'', Australian Mathematical Society Gazette, 36, pp. 50 - 52

Journal articles | 2009

Hirschhorn MD, 2009, 'On recurrences of Fahr and Ringel arising in graph theory', Journal of Integer Sequences, 12, pp. Article 09.6.8

Journal articles | 2008

Baruah ND; Cooper S; Hirschhorn MD, 2008, 'Sums of Squares and sums of triangular numbers induced by partitions of 8', International Journal of Number Theory, 4, pp. 525 - 538

Journal articles | 2008

Hirschhorn MD; Sellers JA, 2008, 'Enumeration of Unigraphical Partitions', Journal of Integer Sequences, 2008

Journal articles | 2008

Hirschhorn MD, 2008, 'A letter from Fitzroy house', American Mathematical Monthly, 115, pp. 563 - 566

Journal articles | 2008

Hirschhorn MD, 2008, 'Pythagoras' Theorem', MATHEMATICAL GAZETTE, 92, pp. 565 - 565, http://dx.doi.org/10.1017/S0025557200183950

Journal articles | 2008

Hirschhorn MD, 2008, 'Three scenarios involving elastic collisions', MATHEMATICAL GAZETTE, 92, pp. 154 - 158, http://dx.doi.org/10.1017/S0025557200182816

Journal articles | 2007

Benjamin AT; Hirschhorn MD, 2007, 'A combinatorial solution to intertwined recurrences', Australasian Journal of Combinatorics, 37, pp. 101 - 116

Journal articles | 2007

Cooper S; Hirschhorn MD, 2007, 'On the number of primitive representations of integers as sums of squares', Ramanujan Journal, 13, pp. 7 - 25

Journal articles | 2007

Hirschhorn MD; Sellers JA, 2007, 'On recent congruence results of Andrews and Paule for broken k-diamonds', Bulletin of the Australian Mathematical Society, 75, pp. 121 - 126

Journal articles | 2007

Hirschhorn MD, 2007, 'Correspondence', MATHEMATICAL GAZETTE, 91, pp. 560 - 560, http://dx.doi.org/10.1017/S0025557200182348

Journal articles | 2007

Hirschhorn MD, 2007, 'Still shorter [2]', Mathematical Intelligencer, 29, pp. 5, http://dx.doi.org/10.1007/BF02986196

Journal articles | 2007

Hirschhorn MD, 2007, 'Teaching Notes Teaching integration', MATHEMATICAL GAZETTE, 91, pp. 547 - 547, http://dx.doi.org/10.1017/S0025557200182294

Journal articles | 2007

Hirschhorn MD, 2007, 'The AM-GM inequality', Mathematical Intelligencer, 29, pp. 7 - 7, http://dx.doi.org/10.1007/BF02986168

Journal articles | 2007

Hirschhorn MD, 2007, 'The alternating harmonic series', Mathematical Intelligencer, 29, pp. 4 - 5

Journal articles | 2006

Cooper S; Hirschhorn M, 2006, 'Sums of squares and sums of triangular numbers', Georgian Mathematical Journal, 13, pp. 675 - 686, http://dx.doi.org/10.1515/GMJ.2006.675

Journal articles | 2006

Hirschhorn MD; Sellers JA, 2006, 'Arithmetic properties of overpartitions into odd parts', Annals of Combinatorics, 10, pp. 353 - 367

Journal articles | 2006

Hirschhorn MD, 2006, '90.04 The number of partitions of a number into distinct squares', MATHEMATICAL GAZETTE, 90, pp. 80 - 87, http://dx.doi.org/10.1017/S0025557200179070

Journal articles | 2006

Hirschhorn MD, 2006, '90.16 Evaluating (sic) (a', MATHEMATICAL GAZETTE, 90, pp. 114 - 116, http://dx.doi.org/10.1017/S0025557200179197

Journal articles | 2006

Hirschhorn MD, 2006, '90.54 The new neighbours problem: a solution', MATHEMATICAL GAZETTE, 90, pp. 321 - 324, http://dx.doi.org/10.1017/S0025557200179884

Journal articles | 2006

Hirschhorn MD, 2006, 'Coupled second-order recurrences', Fibonacci Quarterly, 44, pp. 20 - 25

Journal articles | 2006

Hirschhorn MD, 2006, 'Coupled third-order recurrences', Fibonacci Quarterly, 44, pp. 26 - 31

Journal articles | 2006

Hirschhorn MD, 2006, 'On Euler's constant', MATHEMATICAL GAZETTE, 90, pp. 295 - 298, http://dx.doi.org/10.1017/S002555720017977X

Journal articles | 2006

Hirschhorn MD, 2006, 'The case of the mysterious sevens', International Journal of Number Theory, 2, pp. 213 - 216

Journal articles | 2005

Angell DD; Hirschhorn MD, 2005, 'A remarkable continued fraction', Bulletin of the Australian Mathematical Society, 72, pp. 45 - 52

Journal articles | 2005

Cooper S; Gun S; Hirschhorn MD; Ramakrishnan B, 2005, 'Relations among Fourier coefficients of certain eta products', Integers: the Electronic Journal of Combinatorial Number Theory, 5, pp. A16

Journal articles | 2005

Doust IR; Hirschhorn MD; Ho J, 2005, 'Trigonometric identities, linear algebra, and computer algebra', American Mathematical Monthly, 112, pp. 155 - 164, http://dx.doi.org/10.2307/30037413

Journal articles | 2005

Hirschhorn MD; Sellers JA, 2005, 'An infinite family of overpartition congruences modulo 12', Integers: the Electronic Journal of Combinatorial Number Theory, 5, pp. A20 - A20

Journal articles | 2005

Hirschhorn MD; Sellers JA, 2005, 'Arithmetic relations for overpartitions', Journal of Combinatorial Mathematics and Combinatorial Computing, 53, pp. 65 - 73

Journal articles | 2005

Hirschhorn MD; Sellers JA, 2005, 'Further results for partitions into four squares of equal parity', ARS Combinatoria, 76, pp. 33 - 45

Journal articles | 2005

Hirschhorn MD, 2005, 'An identity involving binomial coefficients', MATHEMATICAL GAZETTE, 89, pp. 256 - 258, http://dx.doi.org/10.1017/S0025557200177745

Journal articles | 2005

Hirschhorn MD, 2005, 'Non-trivial intertwined second-order recurrence relations', Fibonacci Quarterly, 43, pp. 316 - 325

Journal articles | 2005

Hirschhorn MD, 2005, 'On representations of pi and squareroot 2', Australian Mathematical Society Gazette, 32, pp. 124 - 126

Journal articles | 2005

Hirschhorn MD, 2005, 'Ramanujan`s `most beautiful identity`', Australian Mathematical Society Gazette, 32, pp. 259 - 262

Journal articles | 2005

Hirschhorn MD, 2005, 'The number of representations of a number by various forms', Discrete Mathematics, 298, pp. 205 - 211, http://www.sciencedirect.com/science/article/B6V00-4GP7PD7-1/2/36a5fe822a28adf5954b53b42b640cf1

Journal articles | 2004

Cooper S; Hirschhorn MD, 2004, 'A combinatorial proof of a result from number theory', Integers: the Electronic Journal of Combinatorial Number Theory, 4

Journal articles | 2004

Cooper S; Hirschhorn MD, 2004, 'Results of Hurwitz type for three squares', Discrete Mathematics, 274, pp. 9 - 24

Journal articles | 2004

Hirschhorn MD; Sellers JA, 2004, 'A different view of m-ary partitions', Australasian Journal of Combinatorics, 30, pp. 193 - 196

Journal articles | 2004

Hirschhorn MD; Sellers JA, 2004, 'On a problem of Lehmer on partitions into squares', Ramanujan Journal, 8, pp. 279 - 287, http://dx.doi.org/10.1007/s11139-004-0138-0

Journal articles | 2004

Hirschhorn MD; Sellers JA, 2004, 'Partitions into three triangular numbers', Australasian Journal of Combinatorics, 30, pp. 307 - 318

Journal articles | 2004

Sheppard C; Campbell S; Hirschhorn MD, 2004, 'Zernike expansion of separable functions of Cartesian coordinates', Applied Optics, 43, pp. 3963 - 3966

Journal articles | 2002

Barrucand P; Cooper S; Hirschhorn MD, 2002, 'Relations between squares and triangles', Discrete Mathematics, 248, pp. 245 - 247

Journal articles | 2002

Barrucand P; Cooper S; Hirschhorn MD, 2002, 'Results of Hurwitz type for five or more squares', Ramanujan Journal, 6, pp. 347 - 367

Journal articles | 2002

Barrucand P; Hirschhorn MD, 2002, 'Formulae asociated with 5, 7, 9 and 11 squares', Bulletin of the Australian Mathematical Society, 65, pp. 503 - 510

Journal articles | 2002

Brown PG; Hirschhorn MD, 2002, 'A note on the Pell equation x2-(m2-4)y2 =1', Australian Mathematical Society Gazette, 29, pp. 273 - 276

Journal articles | 2002

Hirschhorn MD, 2002, 'Binomial coefficient identities and hyjpergeometric series', Australian Mathematical Society Gazette, 29, pp. 203 - 208

Journal articles | 2002

Hirschhorn MD, 2002, 'K-Gon partitions', Bulletin of the Australian Mathematical Society, 66, pp. 149 - 150

Journal articles | 2002

Hirschhorn MD, 2002, 'On sums of squares', Australian Mathematical Society Gazette, 29, pp. 86 - 87

Journal articles | 2002

Hirschhorn MD, 2002, 'There are infinitely many prime numbers', Australian Mathematical Society Gazette, 29, pp. 103 - 103

Journal articles | 2001

Cooper S; Hirschhorn MD, 2001, 'On some infinite product identities', Rocky Mountain Journal of Mathematics, pp. 131 - 139

Journal articles | 2001

Cooper S; Hirschhorn MD, 2001, 'On some sum-to-product identities', Bulletin of the Australian Mathematical Society, pp. 353 - 365

Journal articles | 2001

Hirschhorn MD, 2001, 'On partitions into four distinct squares of equal parity', Australasian Journal of Combinatorics, 24, pp. 285 - 291

Journal articles | 2001

Hirschhorn MD, 2001, 'On the expansion of a continued fraction of Gordon', Ramanujan Journal, 5, pp. 369 - 375, http://dx.doi.org/10.1023/A:1013939720688

Journal articles | 2000

Cooper S; Hirschhorn MD; Lewis RA, 2000, 'Powers of Euler`s product and related identities', Ramanujan Journal, pp. 137 - 155

Journal articles | 2000

Hirschhorn MD, 2000, 'A proof of Eperson`s conjecture', Mathematical Gazette, pp. 442 - 446

Journal articles | 2000

Hirschhorn MD, 2000, 'An identity of Ramanujan, and applications', Contemporary Mathematics, pp. 229 - 234

Journal articles | 2000

Hirschhorn MD, 2000, 'Arithmetic consequences of Jacobi`s two-squares theorem', Ramanujan Journal, 4, pp. 51 - 57, http://dx.doi.org/10.1023/A:1009877906185

Journal articles | 2000

Hirschhorn MD, 2000, 'How many ways can a king cross the board?', Australian Mathematical Society Gazette, pp. 104 - 106

Journal articles | 2000

Hirschhorn MD, 2000, 'More on Cootie', College Mathematics Journal, pp. 126 - 128

Journal articles | 2000

Hirschhorn MD, 2000, 'Parity results for certain partition functions', Ramanujan Journal, 4, pp. 129 - 135, http://dx.doi.org/10.1023/A:1009874919415

Journal articles | 2000

Hirschhorn MD, 2000, 'Partial fractions and four classical theorems of number theory', American Mathematical Monthly, 107, pp. 260 - 263

Journal articles | 2000

Hirschhorn MD, 2000, 'Partiy results for certain partition functions', Ramanujan Journal, pp. 129 - 135

Journal articles | 2000

Hirschhorn MD, 2000, 'Some formulae for partitions into squares', Discrete Mathematics, 211, pp. 225 - 228, http://dx.doi.org/10.1016/S0012-365X(99)00159-4

Journal articles | 2000

Hirschhorn MD, 2000, 'Triangles with integer sides, revisited', Mathematics Magazine, pp. 53 - 56

Journal articles | 2000

Hirschhorn MD, 2000, 'Winquist and the Atkin- Swinnerton-Dyer partition congruences for modulus 11', Australasian Journal of Combinatorics, 22, pp. 101 - 104

Journal articles | 1999

Hirschhorn A; Hirschhorn MD; Hirschhorn P, 1999, 'The pizza theorem', Australian Mathematical Society Gazette, pp. 120 - 121

Journal articles | 1999

Hirschhorn MD; Sellers JA, 1999, 'On representations of a number as a sum of three squares', Discrete Mathematics, 199, pp. 85 - 101

Journal articles | 1999

Hirschhorn MD; Sellers JA, 1999, 'Some parity results for 16-cores', Ramanujan Journal, 3, pp. 281 - 296, http://dx.doi.org/10.1023/A:1009879303577

Journal articles | 1999

Hirschhorn MD, 1999, 'A problem in dynamics', Australian Mathematical Society Gazette, pp. 34 - 41

Journal articles | 1999

Hirschhorn MD, 1999, 'Another short proof of Ramanujan`s mod 5 partition congruence, and more', American Mathematical Monthly, 106, pp. 580 - 583

Journal articles | 1999

Hirschhorn MD, 1999, 'Basis partitions and Rogers-Ramanujan partitions', Discrete Mathematics, 205, pp. 241 - 243, http://dx.doi.org/10.1016/S0012-365X(99)00030-8

Journal articles | 1999

Hirschhorn MD, 1999, 'Jacobi`s two-square theorem and related identities', Ramanujan Journal, 3, pp. 153 - 158, http://dx.doi.org/10.1023/A:1006993323652

Journal articles | 1999

Hirschhorn MD, 1999, 'The double-angle formulae', Australian Mathematical Society Gazette, pp. 171 - 172

Journal articles | 1998

Hirschhorn MD, 1998, 'A new Formula for Pi', Australian Mathematical Society Gazette, pp. 82 - 83

Journal articles | 1998

Hirschhorn MD, 1998, 'A trigonometric identity and Morley`s theorem', Australian Mathematical Society Gazette, pp. 198 - 199

Journal articles | 1998

Hirschhorn MD, 1998, 'On the expansion of Ramanujan`s continued fraction', Ramanujan Journal, 2, pp. 521 - 527

Journal articles | 1998

Hirschhorn MD, 1998, 'Proofs of some hyperelliptic function identities', Bulletin of the Australian Mathematical Society, pp. 465 - 468

Journal articles | 1998

Hirschhorn MD, 1998, 'The fundamental theorem of algebra', College Mathematics Journal, pp. 276 - 277

Journal articles | 1998

Hirschhorn MD, 1998, 'The sum sqrt 1 + sqrt 2 + ¿ + sqrt n without integration', Australian Mathematical Society Gazette, pp. 143 - 145

Journal articles | 1998

Hirschhorn MD, 1998, 'Three classical results or representations of a number', Seminaire Lotharingien de Combinatoire, pp. 41

Journal articles | 1998

Hirschhorn MD, 1998, 'Two diophantine equations studied by Ramanujan', Mathematics Magazine, pp. 386 - 388

Journal articles | 1998

Hirschhorn MD, 1998, 'Two or three identities of Ramanujan', American Mathematical Monthly, 105, pp. 52 - 54, http://dx.doi.org/10.2307/2589526

Journal articles | 1997

Hirschhorn MD, 1997, 'Radius of a buried pipe', Australian Mathematical Society Gazette, pp. 180 - 181

Journal articles | 1997

Hirschhorn MD, 1997, 'The volume of a cone, without calculus', Mathematics Magazine, pp. 295 - 296

Journal articles | 1996

Hirschhorn MD; Sellers JA, 1996, 'On representations of a number as a sum of three triangles', ACTA Arithmetica, 77, pp. 289 - 301, http://dx.doi.org/10.4064/aa-77-3-289-301

Journal articles | 1996

Hirschhorn MD; Sellers JA, 1996, 'Some amazing facts about 4-cores', Journal of Number Theory, 60, pp. 51 - 69, http://dx.doi.org/10.1006/jnth.1996.0112

Journal articles | 1996

Hirschhorn MD; Sellers JA, 1996, 'Two congruences involving 4-cores', Electronic Journal of Combinatorics, 3, pp. 1 - 8

Journal articles | 1996

Hirschhorn MD, 1996, 'A proof in the spirit of Zeilberger of an amazing identity of Ramanujan', Mathematics Magazine, pp. 267 - 269

Journal articles | 1996

Hirschhorn MD, 1996, 'A reformulation of Ramanujan`s partition congruences', Journal of Combinatorial Theory Series A, 73, pp. 346 - 347, http://dx.doi.org/10.1016/S0097-3165(96)80010-0

Journal articles | 1996

Hirschhorn MD, 1996, 'Calkin`s binomial identity', Discrete Mathematics, 159, pp. 273 - 278, http://dx.doi.org/10.1016/0012-365X(95)00086-C

Journal articles | 1995

Hirschhorn MD, 1995, 'A new proof of an old formula', Bulletin of the ICA, 13, pp. 127

Journal articles | 1995

Hirschhorn MD, 1995, 'An amazing identity of Ramanujan', Mathematics Magazine, pp. 199 - 201

Journal articles | 1994

Hirschhorn MD, 1994, 'Ramanujan's partition congruences', Discrete Mathematics, 131, pp. 351 - 355, http://dx.doi.org/10.1016/0012-365X(94)90397-2

Journal articles | 1994

Hirschhorn MD, 1994, 'Several Identities in Statistical Mechanics', International Journal of Mathematics and Mathematical Sciences, 17, pp. 817 - 820, http://dx.doi.org/10.1155/S0161171294001146

Journal articles | 1993

Hirschhorn MD, 1993, 'On the parity of p(n), II', Journal of Combinatorial Theory, Series A, 62, pp. 128 - 138, http://dx.doi.org/10.1016/0097-3165(93)90075-J

Journal articles | 1988

Hirschhorn MD, 1988, 'A generalisation of the quintuple product identity', Journal of the Australian Mathematical Society, 44, pp. 42 - 45, http://dx.doi.org/10.1017/S1446788700031359

Journal articles | 1987

Hirschhorn MD, 1987, 'A simple proof of Jacobi's four-square theorem', Proceedings of the American Mathematical Society, 101, pp. 436 - 438, http://dx.doi.org/10.1090/S0002-9939-1987-0908644-9

Journal articles | 1985

Hirschhorn MD; Hunt DC, 1985, 'Equilateral convex pentagons which tile the plane', Journal of Combinatorial Theory, Series A, 39, pp. 1 - 18, http://dx.doi.org/10.1016/0097-3165(85)90078-0

Journal articles | 1984

Guttmann AJ; Hirschhorn M, 1984, 'Comment on the number of spiral self-avoiding walks', Journal of Physics A: General Physics, 17, pp. 3613 - 3614, http://dx.doi.org/10.1088/0305-4470/17/18/029

Journal articles | 1983

Hirschhorn MD, 1983, 'A Simple proof of an identity of Ramanujan', Journal of the Australian Mathematical Society, 34, pp. 31 - 35, http://dx.doi.org/10.1017/S1446788700019728

Journal articles | 1982

Hirschhorn MD, 1982, 'A Simple Proof of Jacobi’s Four-Square Theorem', Journal of the Australian Mathematical Society, 32, pp. 61 - 67, http://dx.doi.org/10.1017/S144678870002440X

Journal articles | 1981

Hirschhorn MD; Hunt DC, 1981, 'A simple proof of the Ramanujan conjecture for powers of 5', Journal fur die Reine und Angewandte Mathematik, 1981, pp. 1 - 17, http://dx.doi.org/10.1515/crll.1981.326.1

Journal articles | 1981

Hirschhorn MD, 1981, 'Infinitely many identities of kolberg type', Journal of the Australian Mathematical Society, 31, pp. 20 - 25, http://dx.doi.org/10.1017/S1446788700018450

Journal articles | 1980

Hirschhorn MD, 1980, 'A continued fraction of ramanujan', Journal of the Australian Mathematical Society, 29, pp. 80 - 86, http://dx.doi.org/10.1017/S1446788700020954

Journal articles | 1980

Hirschhorn MD, 1980, 'Two further ramanujan pairs', Journal of the Australian Mathematical Society, 30, pp. 1 - 4, http://dx.doi.org/10.1017/S1446788700021856

Journal articles | 1979

Hirschhorn MD, 1979, 'Some partition theorems of the Rogers-Ramanujan type', Journal of Combinatorial Theory, Series A, 27, pp. 33 - 37, http://dx.doi.org/10.1016/0097-3165(79)90005-0

Journal articles | 1976

Hirschhorn MD, 1976, 'Simple proofs of identities of MacMahon and Jacobi', Discrete Mathematics, 16, pp. 161 - 162, http://dx.doi.org/10.1016/0012-365X(76)90144-8

Journal articles | 1975

Hirschhorn MD; Loxton JH, 1975, 'Congruence properties of the binary partition function', Mathematical Proceedings of the Cambridge Philosophical Society, 78, pp. 437 - 442, http://dx.doi.org/10.1017/S0305004100051896

Journal articles | 1974

Hirschhorn MD, 1974, 'A continued fraction', Duke Mathematical Journal, 41, pp. 27 - 33, http://dx.doi.org/10.1215/S0012-7094-74-04104-0

Journal articles | 1973

Hirschhorn MD, 1973, 'A continued fraction of Carlitz', Duke Mathematical Journal, 40, pp. 77 - 80, http://dx.doi.org/10.1215/S0012-7094-73-04008-8

Journal articles | 1972

Hirschhorn MD, 1972, 'Partitions and ramanujan’s continued fraction', Duke Mathematical Journal, 39, pp. 789 - 791, http://dx.doi.org/10.1215/S0012-7094-72-03986-5
Conference Papers | 2016

Hirschhorn MD, 2016, 'Ramanujan’s tau function', in Springer Proceedings in Mathematics and Statistics, Gainesville, FL, USA, pp. 311 - 328, presented at Analytic Number Theory, Modular Forms and q-Hypergeometric Series, Gainesville, FL, USA, 17 March 2016 - 21 March 2016, http://dx.doi.org/10.1007/978-3-319-68376-8_18

Conference Papers | 1999

Hirschhorn MD; Mcgowan JA, 1999, 'Algebraic consequences of Jacobi`s two- and four-square theorems', in Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, University of Florida, Gainesville, presented at Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, University of Florida, Gainesville, 11 November 1999 - 13 November 1999

Conference Papers | 1999

Hirschhorn MD; Sellers JA, 1999, 'Some relations for partitions into four squares', in international workshop special functions, international workshop special functions, Hong Kong, presented at international workshop special functions, Hong Kong, 21 June 1999 - 25 June 1999

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