Some congruences modulo 3, 5 and 7 for broken \(((r\ell-1)/2)\)-diamond partitions for \(r\in \{3,25,49\}\) and odd positive integer \(\ell\)

DOI10.1016/J.JMAA.2017.12.012zbMath1379.05012OpenAlexW2773192213MaRDI QIDQ681776

Nipen Saikia, Jubaraj Chetry

Publication date: 13 February 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.12.012

zbMATH Keywords

\(q\)-identitiesbroken \(k\)-diamond partitionpartition congruence

Mathematics Subject Classification ID

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

Cites Work

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• Infinite families of congruences modulo 7 for broken 3-diamond partitions
• Congruences for broken \(k\)-diamond partitions
• New parity results for broken 11-diamond partitions
• New congruences modulo powers of 2 for broken 3-diamond partitions and 7-core partitions
• Infinite families of strange partition congruences for broken 2-diamonds
• Two congruences involving Andrews-Paule's broken 3-diamond partitions and 5-diamond partitions
• An extensive analysis of the parity of broken 3-diamond partitions
• Some congruences for Andrews-Paule's broken 2-diamond partitions
• Elementary proofs of Radu and Sellers' results for broken 2-diamond partitions
• Elementary proofs of parity results for broken 3-diamond partitions
• Parity results for broken k-diamond partitions and (2k+1)-cores
• MacMahon's partition analysis XI: Broken diamonds and modular forms
• On recent congruence results of Andrews and Paule for broken k-diamonds
• More parity results for broken 8-diamond partitions

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