A PROOF OF KEITH'S CONJECTURE FOR 9-REGULAR PARTITIONS MODULO 3

DOI10.1142/S1793042113501169zbMath1286.11169OpenAlexW2089517115WikidataQ123269281 ScholiaQ123269281MaRDI QIDQ5408832

Ernest X. W. Xia, Olivia X. M. Yao

Publication date: 11 April 2014

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

Full work available at URL: https://doi.org/10.1142/s1793042113501169

zbMATH Keywords

congruenceregular partition

Mathematics Subject Classification ID

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

Related Items (18)

Parity results for 7-regular and 23-regular partitions ⋮ Congruences for (3,11)-regular bipartitions modulo 11 ⋮ An infinite family of congruences modulo 3 for 13-regular bipartitions ⋮ Ramanujan-type congruences modulo \(m\) for \((l, m)\)-regular bipartitions ⋮ Arithmetic properties for \((s,t)\)-regular bipartition functions ⋮ GENERALISATION OF KEITH’S CONJECTURE ON 9-REGULAR PARTITIONS AND 3-CORES ⋮ Congruences of \(\ell\)-regular partition triples for \(\ell\in\{2, 3, 4, 5\}\) ⋮ Congruences for some \(l\)-regular partitions modulo \(l\) ⋮ New congruences modulo powers of 2 and 3 for 9-regular partitions ⋮ 4-regular partitions and the pod function ⋮ Parity results for 13-regular partitions and broken 6-diamond partitions ⋮ On \(\ell \)-regular bipartitions modulo \(\ell \) ⋮ Arithmetic properties for 7-regular partition triples ⋮ Congruences for \(\ell\)-regular overpartition for \(\ell \in \{5,6,8\}\) ⋮ New infinite families of congruences modulo 8 for partitions with even parts distinct ⋮ Quadratic forms and congruences for \(\ell\)-regular partitions modulo 3, 5 and 7 ⋮ Congruences for 9-regular partitions modulo 3 ⋮ On 3-divisibility of 9- and 27-regular partitions

Cites Work

• Arithmetic of the 13-regular partition function modulo 3
• Arithmetic properties of partitions with even parts distinct
• Congruences for \(\ell\)-regular partition functions modulo 3
• The \(p^{a}\)-regular partition function modulo \(p^{j}\)
• \(l\)-divisibility of \(l\)-regular partition functions
• Divisibility of certain partition functions by powers of primes
• ARITHMETIC OF ℓ-REGULAR PARTITION FUNCTIONS
• ELEMENTARY PROOFS OF VARIOUS FACTS ABOUT 3-CORES

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