Two congruences involving Andrews-Paule's broken 3-diamond partitions and 5-diamond partitions

DOI10.3792/pjaa.87.65zbMath1256.11055arXiv1006.2177OpenAlexW1982639388MaRDI QIDQ719910

Xinhua Xiong

Publication date: 12 October 2011

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.2177

zbMATH Keywords

congruencesmodular formsbroken diamond partitions

Mathematics Subject Classification ID

Partitions; congruences and congruential restrictions (11P83) Congruences for modular and (p)-adic modular forms (11F33) Holomorphic modular forms of integral weight (11F11)

Related Items (20)

Infinite families of congruences modulo 7 for broken 3-diamond partitions ⋮ Congruences modulo 11 for broken 5-diamond partitions ⋮ Congruences for broken \(k\)-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 ⋮ Inequalities for the broken \(k\)-diamond partition functions ⋮ Ramanujan-type congruences for broken 2-diamond partitions modulo 3 ⋮ 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 for broken 3-diamond and 7 dots bracelet partitions ⋮ Congruences modulo 7 for broken 3-diamond partitions ⋮ Extensive parity analysis of broken 5-diamond partitions ⋮ More parity results for broken 8-diamond partitions ⋮ An extensive analysis of the parity of broken 3-diamond partitions ⋮ A note on the parity of broken 7-diamond partitions ⋮ More parity results for broken 9-diamond partitions ⋮ Parity results for broken 5-diamond, 7-diamond and 11-diamond 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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• Infinite families of strange partition congruences for broken 2-diamonds
• Some congruences for Andrews-Paule's broken 2-diamond partitions
• Congruences for Frobenius partitions
• MacMahon's partition analysis XI: Broken diamonds and modular forms
• On recent congruence results of Andrews and Paule for broken k-diamonds
• Construction and Application of a Class of Modular Functions (II)†
• Ramanujan-type congruences for three colored Frobenius partitions
• MacMahon's partition analysis. VIII: Plane partition diamonds

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