Some congruences for Andrews-Paule's broken 2-diamond partitions

DOI10.1016/j.disc.2007.10.050zbMath1206.05020OpenAlexW2087957013MaRDI QIDQ998456

Song Heng Chan

Publication date: 28 January 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2007.10.050

zbMATH Keywords

partition functioncongruencesplane partitionsbroken diamonds

Mathematics Subject Classification ID

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

Related Items (32)

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 ⋮ Turán inequalities for the broken \(k\)-diamond partition functions ⋮ Infinite families of strange partition congruences for broken 2-diamonds ⋮ New parity results for broken 11-diamond partitions ⋮ New congruences modulo powers of 2 for broken 3-diamond partitions and 7-core partitions ⋮ Pairs of partitions without repeated odd parts ⋮ Inequalities for the broken \(k\)-diamond partition functions ⋮ Ramanujan-type congruences for broken 2-diamond partitions modulo 3 ⋮ An algorithmic approach to Ramanujan-Kolberg identities ⋮ On the computation of identities relating partition numbers in arithmetic progressions with eta quotients: an implementation of Radu's algorithm ⋮ 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 ⋮ Broken 2-diamond partitions modulo 5 ⋮ Congruences for broken 3-diamond and 7 dots bracelet partitions ⋮ On the parity of broken \(k\)-diamond partitions ⋮ Congruences for bipartitions with odd parts distinct ⋮ Extensive parity analysis of broken 5-diamond partitions ⋮ New congruences for broken $k$-diamond partitions ⋮ Two congruences involving Andrews-Paule's broken 3-diamond partitions and 5-diamond partitions ⋮ More parity results for broken 8-diamond partitions ⋮ An extensive analysis of the parity of broken 3-diamond partitions ⋮ Finding modular functions for Ramanujan-type identities ⋮ More parity results for broken 9-diamond partitions ⋮ An algorithmic approach to Ramanujan's congruences ⋮ 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 ⋮ CONGRUENCES FOR k DOTS BRACELET PARTITION FUNCTIONS

Uses Software

• Omega

Cites Work

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• A trinomial analogue of Bailey's lemma and \(N=2\) superconformal invariance
• Partition identities and congruences associated with the Fourier coefficients of the Euler products.
• MacMahon's partition analysis XI: Broken diamonds and modular forms
• On recent congruence results of Andrews and Paule for broken k-diamonds
• An odd square as a sum of an odd number of odd squares
• Some Properties of p(n) and c(n) Modulo Powers of 13
• Ramanujan Identities Involving the Partition Function for the Moduli 11 a
• MacMahon's partition analysis. VIII: Plane partition diamonds

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