Proofs of some conjectures on the reciprocals of the Ramanujan-Gordon identities

DOI10.1007/s11139-019-00247-9zbMath1491.11094OpenAlexW3042431281WikidataQ113900581 ScholiaQ113900581MaRDI QIDQ2038993

Ernest X. W. Xia, Dazhao Tang, Fanggang Xue, Min Bian

Publication date: 7 July 2021

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

Full work available at URL: https://doi.org/10.1007/s11139-019-00247-9

zbMATH Keywords

partitionscongruencesNewman's identitiesproduct-to-sum identitiesRamanujan's modular equation

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83)

Related Items (2)

MacMahon's partition analysis. XIV: Partitions with \(n\) copies of \(n\) ⋮ Congruences modulo powers of 2 for restricted partition triples due to Lin and Wang

Cites Work

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• Congruences modulo 9 and 27 for overpartitions
• New Ramanujan type congruences modulo 5 for overpartitions
• Partitions in 3 colours
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• Proof of a conjecture on a congruence modulo 243 for overpartitions
• Ramanujan-style proof of \(p_{-3}(11n+7) \equiv 0 \pmod{11}\)
• SOME IDENTITIES IN COMBINATORIAL ANALYSIS
• Congruences modulo 5 for the number of spin characters of the double covers of the symmetric and alternating groups
• Proofs of some conjectures of Sun on the relations between sums of squares and sums of triangular numbers
• Exceptional congruences for powers of the partition function
• Congruences for the reciprocals of the Ramanujan–Gordon identities
• Proof of a conjecture of Hirschhorn and Sellers on overpartitions
• ARITHMETIC PROPERTIES OF 1-SHELL TOTALLY SYMMETRIC PLANE PARTITIONS

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