A variation of the Andrews-Stanley partition function and two interesting \(q\)-series identities

DOI10.1007/s11139-020-00315-5zbMath1477.05009OpenAlexW3087377293MaRDI QIDQ2240501

Lin Peng, Pee Choon Toh, Bernard L. S. Lin

Publication date: 4 November 2021

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-020-00315-5

zbMATH Keywords

partitionsRamanujan's congruencesStanley's partition function

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) (q)-calculus and related topics (05A30) Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83)

Uses Software

• StanBij.mws

Cites Work

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• On certain pairs of \(q\)-series identities
• A four-parameter partition identity
• A general transformation for theta series associated with the quadratic form \(x^2+ky^2\)
• A combinatorial proof of a partition identity of Andrews and Stanley
• On a partition function of Richard Stanly
• On partition functions of Andrews and Stanley
• On Stanley's partition function
• Some interesting \(q\)-series identities
• Some remarks on sign-balanced and maj-balanced posets
• Dissecting the Stanley partition function
• The Andrews-Stanley partition function and $p(n)$: congruences
• On the Andrews-Stanley refinement of Ramanujan’s partition congruence modulo 5 and generalizations

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