By Dr Mike Hirschhorn

Books

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

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

Book Chapters

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

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

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

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

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

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

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

Hirschhorn MD, 2019, 'Two remarkable q-series expansions', Ramanujan Journal, 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, 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, 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, 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, 56, pp. 32 - 37, http://dx.doi.org/10.1080/00150517.2018.12427718

Hirschhorn MD, 2018, 'Partitions in 3 colours', Ramanujan Journal, 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, 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, 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, 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, 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, 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, 53, pp. 319 - 322, http://dx.doi.org/10.1080/00150517.2015.12428250

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Hirschhorn MD, 2013, 'A constant in a formula of Ramanujan', Mathematical Gazette, 97, pp. 276

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

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

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

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

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

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

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

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

Hirschhorn MD, 2012, 'Inequalities for Euler's constant', Mathematical Gazette, 96, pp. 133 - 136

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

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

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