Some identities for Lin-Peng-Toh's \(k\)-colored partition statistic

DOI10.1007/s11139-023-00807-0arXiv2308.05931OpenAlexW4390533512MaRDI QIDQ6200991

Yang Lin, Xuan Yu, Ernest X. W. Xia

Publication date: 25 March 2024

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

Full work available at URL: https://arxiv.org/abs/2308.05931

zbMATH Keywords

partitionscrankrankAndrews-Beck type congruences

Mathematics Subject Classification ID

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

Cites Work

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• On a generalized crank for \(k\)-colored partitions
• Variations of Andrews-Beck type congruences
• Weighted generalized crank moments for \(k\)-colored partitions and 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 the total number of parts functions associated with ranks of partitions modulo 5 and 7
• Proof of a Lin-Peng-Toh's conjecture on an Andrews-Beck type congruence
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• 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
• The Ramanujan–Dyson identities and George Beck’s congruence conjectures
• A proof of Mao's conjecture on an identity of Beck's partition statistics
• On the total number of ones of partitions associated to cranks
• Proofs of two conjectural Andrews–Beck type congruences due to Lin, Peng and Toh
• Andrews-Beck type congruences modulo 2 and 4 for Beck's partition statistics

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