Select Publications

Books

Hirschhorn MD, 2017, The Power of q A Personal Journey, Springer

Book Chapters

Chern S; Hirschhorn MD, 2021, 'Partitions into Distinct Parts Modulo Powers of 5', in Trends in Mathematics, pp. 305 - 328, http://dx.doi.org/10.1007/978-3-030-57050-7_17

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

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

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

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

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

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

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

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

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

Hirschhorn MD, 2018, 'Congruences modulo 5 for partitions into at most four parts', Fibonacci Quarterly, vol. 56, pp. 32 - 37

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

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

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

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

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

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

Hirschhorn MD, 2015, 'Binomial identities and congruences for Euler numbers', Fibonacci Quarterly, vol. 53, pp. 319 - 322

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

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

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

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

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

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

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

Hirschhorn MD, 2014, 'Stirling without Wallis', Fibonacci Quarterly, vol. 52, pp. 321 - 324

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

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

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

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

Hirschhorn MD, 2014, 'The number of different parts in the partitions of n', Fibonacci Quarterly, vol. 52, pp. 10 - 15

Hirschhorn MD, 2013, 'The number of 1's in the partitions of n', Fibonacci Quarterly, vol. 51, pp. 326 - 329

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

Hirschhorn MD, 2013, 'Estimating the apery numbers II', Fibonacci Quarterly, vol. 51, pp. 215 - 217

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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