Linear inequalities concerning the sum of the distinct parts congruent to r modulo m in all the partitions of n

DOI10.2989/16073606.2023.2174911MaRDI QIDQ6070474

Mircea Merca

Publication date: 21 November 2023

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

zbMATH Keywords

integer partitionspartition inequalitiespartition identitiestruncated theta series

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83)

Cites Work

• The truncated pentagonal number theorem
• Weighted Rogers-Ramanujan partitions and Dyson crank
• Asymptotically trivial linear homogeneous partition inequalities
• Truncated theta series and a problem of Guo and Zeng
• Fast algorithm for generating ascending compositions
• Two truncated identities of Gauss
• Polygonal numbers and Rogers-Ramanujan-Gordon theorem
• Linear inequalities concerning partitions into distinct parts
• Bisected theta series, least \(r\)-gaps in partitions, and polygonal numbers
• A truncated theta identity of Gauss and overpartitions into odd parts
• A general method for proving the non-trivial linear homogeneous partition inequalities
• Dyson’s crank of a partition
• On the sum of parts with multiplicity at least 2 in all the partitions of n
• Some Properties of Partitions
• Refinement of some partition identities of Merca and Yee
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