Congruences modulo 11 for broken 5-diamond partitions

DOI10.1007/S11139-017-9894-5zbMath1448.11183OpenAlexW2609900324MaRDI QIDQ1635630

James A. Sellers, Ernest X. W. Xia, Eric H. Liu

Publication date: 31 May 2018

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

Full work available at URL: https://doi.org/10.1007/s11139-017-9894-5

zbMATH Keywords

theta functioncongruencebroken \(k\)-diamond partition

Mathematics Subject Classification ID

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

Cites Work

• Infinite families of congruences modulo 7 for broken 3-diamond partitions
• More infinite families of congruences modulo 5 for broken 2-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
• Newman's identity and infinite families of congruences modulo 7 for broken 3-diamond partitions
• Congruences for broken 3-diamond and 7 dots bracelet 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

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