Combinatorial interpretations of congruences for the spt-function

DOI10.1007/s11139-012-9369-7zbMath1256.05012OpenAlexW2097256585MaRDI QIDQ1927653

Frank G. Garvan, Jie Liang, George E. Andrews

Publication date: 2 January 2013

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

Full work available at URL: https://doi.org/10.1007/s11139-012-9369-7

zbMATH Keywords

partitionscrankcongruencesrankbasic hypergeometric seriesRamanujan's lost notebookvector partitionsspt-function

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences for modular and (p)-adic modular forms (11F33) Elementary theory of partitions (11P81) Analytic theory of partitions (11P82) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (19)

Exotic Bailey-Slater spt-functions. II: Hecke-Rogers-type double sums and Bailey pairs from groups A, C, E ⋮ Higher order smallest parts functions and rank-Crank moment inequalities from Bailey pairs ⋮ Exotic Bailey–Slater spt-functions III: Bailey pairs from groups B, F, G, and J ⋮ Exotic Bailey-Slater spt-functions. I: Group A. ⋮ The spt-crank for overpartitions ⋮ Effective estimates for the smallest parts function ⋮ Inequalities between first moments of \(M_2\)-rank and crank for overpartitions ⋮ Partitions and the grand canonical ensemble ⋮ Inequalities between odd moments of rank and crank for overpartitions ⋮ On the distribution of the \textsf{spt}-crank ⋮ Asymptotic formulas for spt-crank of partitions ⋮ On spt-crank-type functions ⋮ Algebraic and transcendental formulas for the smallest parts function ⋮ Proof of the Andrews-Dyson-Rhoades conjecture on the spt-crank ⋮ On the non-negativity of the spt-crank for partitions without repeated odd parts ⋮ Euler-like recurrences for smallest parts functions ⋮ Universal mock theta functions and two-variable Hecke-Rogers identities ⋮ Unimodality of the Andrews-Garvan-Dyson cranks of partitions ⋮ Generating functions and congruences for some partition functions related to mock theta functions

Cites Work

• Cranks---really, the final problem
• Partitions, Durfee symbols, and the Atkin-Garvan moments of ranks
• Partitions and indefinite quadratic forms.
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• Self-conjugate vector partitions and the parity of the spt-function
• Some Properties of Partitions
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