Mappings and symmetries of partitions

DOI10.1016/0097-3165(89)90043-5zbMath0682.05008OpenAlexW2023497974MaRDI QIDQ1823942

Freeman J. Dyson

Publication date: 1989

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(89)90043-5

zbMATH Keywords

vector partition

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Elementary theory of partitions (11P81)

Related Items (33)

Asymptotic formulas for \(M_{2}\)-ranks of partitions without repeated odd parts ⋮ Generalization of Dyson's rank and non-Rogers-Ramanujan partitions ⋮ Generalized higher order spt-functions ⋮ Partition bijections, a survey ⋮ Taylor coefficients of mock-Jacobi forms and moments of partition statistics ⋮ Inequalities between ranks and cranks ⋮ On a generalized crank for \(k\)-colored partitions ⋮ Asymptotic formulas for spt-crank of partitions ⋮ The crank moments weighted by the parity of cranks ⋮ Eventual log-concavity of \(k\)-rank statistics for integer partitions ⋮ Explicit congruences for \(k\)-marked Durfee symbols ⋮ UNIFORM ASYMPTOTIC FORMULAS FOR RESTRICTED BIPARTITE PARTITIONS ⋮ Unnamed Item ⋮ Unnamed Item ⋮ REFINEMENTS OF THE FIRST AND SECOND POSITIVE CRANK MOMENTS ⋮ Proof of the Andrews-Dyson-Rhoades conjecture on the spt-crank ⋮ Untrodden pathways in the theory of the restricted partition function \(p(n,N)\) ⋮ CONGRUENCES FOR ANDREWS' SMALLEST PARTS PARTITION FUNCTION AND NEW CONGRUENCES FOR DYSON'S RANK ⋮ On some relations between the rank and the crank ⋮ Dyson's ranks and Appell-Lerch sums ⋮ Higher order SPT functions for overpartitions, overpartitions with smallest part even, and partitions with smallest part even and without repeated odd parts ⋮ Asymptotic inequalities for \(k\)-ranks and their cumulation functions ⋮ On Dyson’s crank conjecture and the uniform asymptotic behavior of certain inverse theta functions ⋮ Unimodality of the Andrews-Garvan-Dyson cranks of partitions ⋮ Rank and crank moments for overpartitions ⋮ ON THE DISTRIBUTION OF THE RANK STATISTIC FOR STRONGLY CONCAVE COMPOSITIONS ⋮ On the distribution of rank and crank statistics for integer partitions ⋮ Moments of ranks and cranks, and quotients of Eisenstein series and the Dedekind eta function ⋮ Dyson's crank and unimodal compositions ⋮ Quasimodularity of the kth residual cranks ⋮ An inequality between finite analogues of rank and crank moments ⋮ Some observations on Dyson's new symmetries of partitions ⋮ Uniform asymptotic formulas for the Fourier coefficients of the inverse of theta functions

Cites Work

• CONGRUENCES FOR ANDREWS' SMALLEST PARTS PARTITION FUNCTION AND NEW CONGRUENCES FOR DYSON'S RANK
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• On the Geometry of Numbers in Elementary Number Theory
• A new symmetry of partitions

This page was built for publication: Mappings and symmetries of partitions