A proof of Mao's conjecture on an identity of Beck's partition statistics

DOI10.1007/s11139-022-00692-zOpenAlexW4321611155WikidataQ123025146 ScholiaQ123025146MaRDI QIDQ6054921

Ernest X. W. Xia, Renrong Mao

Publication date: 28 September 2023

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

Full work available at URL: https://doi.org/10.1007/s11139-022-00692-z

zbMATH Keywords

partitioncrankrankBeck's partition statistics

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Elementary theory of partitions (11P81)

Related Items (5)

On the total number of ones of partitions associated to cranks ⋮ Some identities on Beck's partition statistics ⋮ Andrews-Beck type congruences modulo 2 and 4 for Beck's partition statistics ⋮ A modular approach to Andrews-Beck partition statistics ⋮ Some identities for Lin-Peng-Toh's \(k\)-colored partition statistic

Cites Work

• The generating functions of the rank and crank modulo 8
• Variations of Andrews-Beck type congruences
• Weighted partition rank and crank moments. II: Odd-order moments
• Proofs of some conjectures of Chan-Mao-Osburn on Beck's partition statistics
• On total number parts functions associated to ranks of overpartitions
• Dyson’s crank of a partition
• Weighted partition rank and crank moments. III. A list of Andrews–Beck type congruences modulo 5, 7, 11 and 13
• Generalized Lambert series identities
• Some Properties of Partitions
• The Ramanujan–Dyson identities and George Beck’s congruence conjectures
• A mock theta function identity related to the partition rank modulo 3 and 9
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