MacMahon's partition analysis XIII: Schmidt type partitions and modular forms

DOI10.1016/j.jnt.2021.09.008zbMath1484.11201OpenAlexW3210926644WikidataQ114156724 ScholiaQ114156724MaRDI QIDQ2071693

George E. Andrews, Paule, Peter

Publication date: 28 January 2022

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2021.09.008

zbMATH Keywords

partitions\(q\)-seriespartition congruencesMacMahon's partition analysismodular forms and modular functionsRadu's Ramanujan-Kolberg algorithm

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Modular and automorphic functions (11F03) Dedekind eta function, Dedekind sums (11F20) Computational number theory (11Y99)

Related Items

A combinatorial proof of a Schmidt type theorem of Andrews and Paule ⋮ Diagonal hooks and a Schmidt-type partition identity ⋮ Elementary proofs of infinitely many congruences for \(k\)-elongated partition diamonds ⋮ Congruences for k-elongated plane partition diamonds ⋮ More on Schmidt's partition theorem ⋮ Schmidt type partitions ⋮ Interview with Peter Paule ⋮ Schmidt-type theorems via weighted partition identities ⋮ Exact \(\mathcal{N} = 2^\ast\) Schur line defect correlators ⋮ On the divisibility of 7-elongated plane partition diamonds by powers of 8 ⋮ The minimal excludant and Schmidt's partition theorem ⋮ A general class of Schmidt theorems ⋮ MacMahon's partition analysis. XIV: Partitions with \(n\) copies of \(n\) ⋮ Large \(N\) and large representations of Schur line defect correlators ⋮ A congruence family for 2-elongated plane partitions: an application of the localization method ⋮ Weighted cylindric partitions

Uses Software

• Omega
• QEta

Cites Work

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• MacMahon's partition analysis. VIII: Plane partition diamonds