An extensive analysis of the parity of broken 3-diamond partitions

DOI10.1016/j.jnt.2013.05.009zbMath1315.11090OpenAlexW2065509823WikidataQ40002723 ScholiaQ40002723MaRDI QIDQ740907

James A. Sellers, Silviu Radu

Publication date: 9 September 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2013.05.009

zbMATH Keywords

partitionscongruencesmodular formsbroken \(k\)-diamonds

Mathematics Subject Classification ID

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

Related Items (15)

Infinite families of congruences modulo 7 for broken 3-diamond partitions ⋮ Congruences modulo 11 for broken 5-diamond partitions ⋮ More infinite families of congruences modulo 5 for broken 2-diamond partitions ⋮ Elementary proofs of parity results for broken 3-diamond partitions ⋮ Newman's identity and infinite families of congruences modulo 7 for broken 3-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 ⋮ 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 \(\ell\) ⋮ Congruences modulo 4 for broken \(k\)-diamond partitions ⋮ Congruences for broken 3-diamond and 7 dots bracelet partitions ⋮ Parity results for broken 11-diamond partitions ⋮ More parity results for broken 8-diamond partitions ⋮ Parity results for broken 5-diamond, 7-diamond and 11-diamond partitions ⋮ New congruences for broken \(k\)-diamond and \(k\) dots bracelet partitions ⋮ Elementary proofs of Radu and Sellers' results for broken 2-diamond partitions

Cites Work

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• Infinite families of strange partition congruences for broken 2-diamonds
• Two congruences involving Andrews-Paule's broken 3-diamond partitions and 5-diamond partitions
• Some congruences for Andrews-Paule's broken 2-diamond partitions
• An algorithmic approach to Ramanujan's congruences
• Parity results for broken k-diamond partitions and (2k+1)-cores
• A proof of Subbarao's conjecture
• MacMahon's partition analysis XI: Broken diamonds and modular forms
• On recent congruence results of Andrews and Paule for broken k-diamonds

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