New congruences for \(\ell \)-regular partitions for \(\ell \in \{5,6,7,49\}\)

DOI10.1007/S11139-015-9752-2zbMath1415.11137OpenAlexW2294698342MaRDI QIDQ312446

Nayandeep Deka Baruah, Zakir Hussain Ahmed

Publication date: 15 September 2016

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

Full work available at URL: https://doi.org/10.1007/s11139-015-9752-2

zbMATH Keywords

congruence\(\ell \)-regular partition\(p\)-dissection

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83)

Related Items (15)

Congruences for 7 and 49-regular partitions modulo powers of 7 ⋮ Congruences of \(\ell\)-regular partition triples for \(\ell\in\{2, 3, 4, 5\}\) ⋮ On 9-regular bipartitions with distinct even parts ⋮ 6-regular partitions: new combinatorial properties, congruences, and linear inequalities ⋮ On \(m\)-regular partitions in \(k\)-colors ⋮ Arithmetic properties for 7-regular partition triples ⋮ Unnamed Item ⋮ Some congruences modulo 2, 8 and 12 for Andrews' singular overpartitions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Some new congruences for Andrews' singular overpartitions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ New parity results of sums of partitions and squares in arithmetic progressions

Cites Work

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• Arithmetic properties of \(\ell\)-regular partitions
• Quadratic forms and congruences for \(\ell\)-regular partitions modulo 3, 5 and 7
• Arithmetic of the 7-regular bipartition function modulo 3
• Arithmetic of the 13-regular partition function modulo 3
• Congruences for \(\ell\)-regular partition functions modulo 3
• Infinite families of infinite families of congruences for \(k\)-regular partitions
• \(l\)-divisibility of \(l\)-regular partition functions
• An infinite family of congruences modulo 3 for 13-regular bipartitions
• Parity results for 7-regular and 23-regular partitions

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