MacMahon's partition analysis XIII: Schmidt type partitions and modular forms
type: Item
instance of: scholarly article
title: MacMahon's partition analysis XIII: Schmidt type partitions and modular forms
zbMATH Open document ID: 1484.11201
author: George E. Andrews
author: Peter Paule
published in: Journal of Number Theory
publication date: 2022-01-28T00:00:00Z
review text: The study of MacMahon's partition analysis has been the topic of twelve papers written by these two prolific authors. This article has been inspired by a problem of Frank Schmidt related to interrupted partitions. The authors provide a context for this result which leads directly to many other theorems of this nature. Thus, a number of Schmidt type partitions arising from partitions on various graphs will be seen to have modular forms as generating functions. Some conjectures concerning congruences living on arithmetic subsequences of Schmidt type partition numbers are stated. This paper spurs the interest to find further natural arithmetic/combinatorial objects generated by modular forms.
reviewed by: Mircea Merca
Mathematics Subject Classification ID: 11P83
Mathematics Subject Classification ID: 11F20
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 11F03
Mathematics Subject Classification ID: 11Y99
zbMATH DE Number: 7466544
zbMATH Keywords: partitions
zbMATH Keywords: \(q\)-series
zbMATH Keywords: MacMahon's partition analysis
zbMATH Keywords: modular forms and modular functions
zbMATH Keywords: partition congruences
zbMATH Keywords: Radu's Ramanujan-Kolberg algorithm
Wikidata QID: Q114156724
describes a project that uses: QEta
describes a project that uses: Omega
MaRDI profile type: Publication
full work available at URL: j.jnt.2021.09.008
OpenAlex ID: W3210926644
cites work: Q4218535
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DOI: 10.1016/J.JNT.2021.09.008
description: scientific article; zbMATH DE number 7466544