The spt-crank for overpartitions

DOI10.4064/aa166-2-3zbMath1316.11093arXiv1311.3680OpenAlexW2962864064MaRDI QIDQ2928542

Frank G. Garvan, Chris Jennings-Shaffer

Publication date: 7 November 2014

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.3680

zbMATH Keywords

partitionscongruencesoverpartitionsBailey pairssmallest parts functionAndrews' spt-functionmarked partitions

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Modular and automorphic functions (11F03) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Analytic theory of partitions (11P82)

Related Items (17)

The first positive rank and crank moments for overpartitions ⋮ 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. ⋮ Inequalities between first moments of \(M_2\)-rank and crank for overpartitions ⋮ Inequalities between odd moments of rank and crank for overpartitions ⋮ On spt-crank-type functions ⋮ A characterization of congruences modulo 4 on a SPT function of overpartitions ⋮ Another SPT crank for the number of smallest parts in overpartitions with even smallest part ⋮ Asymptotic formulas related to the \(M_2\)-rank of partitions without repeated odd parts ⋮ On the non-negativity of the spt-crank for partitions without repeated odd parts ⋮ Higher order SPT functions for overpartitions, overpartitions with smallest part even, and partitions with smallest part even and without repeated odd parts ⋮ Universal mock theta functions and two-variable Hecke-Rogers identities ⋮ Overpartition rank differences modulo 7 by Maass forms ⋮ Monotonicity properties for ranks of overpartitions ⋮ Legendre theorems for subclasses of overpartitions

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