Divisibility of certain partition functions by powers of primes
From MaRDI portal
Publication:1127624
DOI10.1023/A:1009711020492zbMath0907.11036OpenAlexW1559932750WikidataQ105723372 ScholiaQ105723372MaRDI QIDQ1127624
Publication date: 9 February 1999
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1023/a:1009711020492
Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83)
Related Items (66)
Lacunary eta-quotients modulo powers of primes ⋮ The overpartition function modulo small powers of 2 ⋮ 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 ⋮ GENERALISATION OF KEITH’S CONJECTURE ON 9-REGULAR PARTITIONS AND 3-CORES ⋮ 2-ADIC PROPERTIES OF CERTAIN MODULAR FORMS AND THEIR APPLICATIONS TO ARITHMETIC FUNCTIONS ⋮ Congruences for Andrews' \((k,i)\)-singular overpartitions ⋮ Parity of the coefficients of certain eta-quotients ⋮ Arithmetic properties of cubic and overcubic partition pairs ⋮ Bisected theta series, least \(r\)-gaps in partitions, and polygonal numbers ⋮ Arithmetic properties of \(\ell\)-regular partitions ⋮ Generalisations of Capparelli's and Primc's identities. I: Coloured Frobenius partitions and combinatorial proofs ⋮ Arithmetic properties of partitions with even parts distinct ⋮ Congruences for \(\ell\)-regular partitions and bipartitions ⋮ -REGULAR PARTITIONS AND MODULAR FORMS WITH COMPLEX MULTIPLICATION ⋮ New congruences modulo powers of 2 and 3 for 9-regular partitions ⋮ Certain Diophantine equations and new parity results for 21-regular partitions ⋮ 4-regular partitions and the pod function ⋮ Arithmetic properties of 3-regular 6-tuple partitions ⋮ Congruences modulo powers of 5 for two restricted bipartitions ⋮ Parity results for 13-regular partitions and broken 6-diamond partitions ⋮ On \(\ell \)-regular bipartitions modulo \(\ell \) ⋮ Parity of sums of partition numbers and squares in arithmetic progressions ⋮ Parity of the coefficients of certain eta-quotients. II: The case of even-regular partitions ⋮ A CONJECTURE OF MERCA ON CONGRUENCES MODULO POWERS OF 2 FOR PARTITIONS INTO DISTINCT PARTS ⋮ Congruence properties modulo powers of 2 for overpartitions and overpartition pairs ⋮ Parity results for 9-regular partitions ⋮ New infinite families of congruences modulo 8 for partitions with even parts distinct ⋮ Congruences for \(\ell\)-regular partition functions modulo 3 ⋮ Quadratic forms and congruences for \(\ell\)-regular partitions modulo 3, 5 and 7 ⋮ Arithmetic of the 7-regular bipartition function modulo 3 ⋮ Certain eta-quotients and arithmetic density of Andrews' singular overpartitions ⋮ Partition identities involving gaps and weights ⋮ Arithmetic properties of 3-regular partitions with distinct odd parts ⋮ Congruences for 5-regular partitions modulo powers of 5 ⋮ Congruences for 9-regular partitions modulo 3 ⋮ A PROOF OF KEITH'S CONJECTURE FOR 9-REGULAR PARTITIONS MODULO 3 ⋮ Arithmetic properties of 7-regular partitions ⋮ A new look on the generating function for the number of divisors ⋮ Overpartition pairs modulo powers of 2 ⋮ Arithmetic of the 13-regular partition function modulo 3 ⋮ The \(p^{a}\)-regular partition function modulo \(p^{j}\) ⋮ Congruences for 9-regular partitions modulo 3 ⋮ Divisibility and distribution of partitions into distinct parts ⋮ Number theoretic properties of generating functions related to Dyson’s rank for partitions into distinct parts ⋮ ARITHMETIC OF ℓ-REGULAR PARTITION FUNCTIONS ⋮ On the density of the odd values of the partition function ⋮ The arithmetic of partitions into distinct parts ⋮ On the distribution of odd values of \(2^a\)-regular partition functions ⋮ Infinite families of infinite families of congruences for \(k\)-regular partitions ⋮ THE 7-REGULAR AND 13-REGULAR PARTITION FUNCTIONS MODULO 3 ⋮ 11-Regular partitions and a Hecke eigenform ⋮ Some congruences for $(s,t)$-regular bipartitions modulo $t$ ⋮ Divisibility of Andrews' singular overpartitions by powers of 2 and 3 ⋮ Certain eta-quotients and \(\ell \)-regular overpartitions ⋮ \(l\)-divisibility of \(l\)-regular partition functions ⋮ INDUCTIVE FORMULAS FOR SOME ARITHMETIC FUNCTIONS ⋮ On Andrews' integer partitions with even parts below odd parts ⋮ A new analogue of $t$-core partitions ⋮ The 2-adic behavior of the number of partitions into distinct parts ⋮ Congruences modulo powers of 11 for some partition functions ⋮ ARITHMETIC PROPERTIES OF -REGULAR BIPARTITIONS ⋮ On 3-divisibility of 9- and 27-regular partitions ⋮ On the work of Basil Gordon
This page was built for publication: Divisibility of certain partition functions by powers of primes
