On the Andrews-Stanley refinement of Ramanujan’s partition congruence modulo 5 and generalizations
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Publication:5705529
DOI10.1090/S0002-9947-05-03751-7zbMath1088.11073arXivmath/0401012OpenAlexW1693715085MaRDI QIDQ5705529
Alexander Berkovich, Frank G. Garvan
Publication date: 9 November 2005
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0401012
Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Elementary theory of partitions (11P81)
Related Items (16)
On partitions with fixed number of even-indexed and odd-indexed odd parts ⋮ Multiplication theorems for self-conjugate partitions ⋮ Some generating functions and inequalities for the andrews–stanley partition functions ⋮ Asymptotics, Turán inequalities, and the distribution of the BG-rank and 2-quotient rank of partitions ⋮ K. Saito's Conjecture for nonnegative eta products and analogous results for other infinite products ⋮ The Andrews-Stanley partition function and $p(n)$: congruences ⋮ A variation of the Andrews-Stanley partition function and two interesting \(q\)-series identities ⋮ On \(t\)-core towers and \(t\)-defects of partitions ⋮ The BG-rank of a partition and its applications ⋮ On certain unimodal sequences and strict partitions ⋮ New identities for 7-cores with prescribed BG-rank ⋮ Combining hook length formulas and BG-ranks for partitions via the Littlewood decomposition ⋮ On identities of Watson type ⋮ On the representations of integers by the sextenary quadratic form \(x^2+y^2+z^2+7s^2+7t^2+7u^2\) and 7-cores ⋮ Dissecting the Stanley partition function ⋮ Multiplication theorems for self-conjugate partitions
Uses Software
Cites Work
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- On partition functions of Andrews and Stanley
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- More cranks andt-cores
- The Crank of Partitions Mod 8, 9 and 10
- New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
- Dyson’s crank of a partition
- Cubic Analogues of the Jacobian Theta Function θ(z, q)
- Modular representations of symmetric groups
- Some Properties of Partitions
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