Integer partitions with even parts below odd parts and the mock theta functions

DOI10.1007/s00026-018-0398-9zbMath1455.11139OpenAlexW2884555508WikidataQ114231911 ScholiaQ114231911MaRDI QIDQ1787955

George E. Andrews

Publication date: 5 October 2018

Published in: Annals of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00026-018-0398-9

zbMATH Keywords

partitionscrankmock theta functions

Mathematics Subject Classification ID

Partitions; congruences and congruential restrictions (11P83) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Elementary theory of partitions (11P81) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (19)

A Bijection Between Two Different Classes of Partitions Enumerated by $p_\nu(n)$ ⋮ Generalizations of the Andrews-Yee identities associated with the mock theta functions \(\omega (q)\) and \(\nu (q)\) ⋮ Note on partitions with even parts below odd parts ⋮ On the parity of the number of (a,b,m)-copartitions of n ⋮ Copartitions ⋮ Ramanujan's theta functions and parity of parts and cranks of partitions ⋮ Congruence modulo 4 for Andrews' even parts below odd parts partition function ⋮ Partition congruences and vanishing coefficients of products of theta functions ⋮ Positive differences of overpartitions with separated parts ⋮ Congruences modulo powers of 2 for restricted partition triples due to Lin and Wang ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Some Congruences for Andrews’ Partition Function EO(n) ⋮ Partitions with parts separated by parity ⋮ Combinatorial proofs for identities related to generalizations of the mock theta functions \(\omega (q)\) and \(\nu (q)\) ⋮ A bijective proof of a false theta function identity from Ramanujan's lost notebook ⋮ On a problem of George Andrews concerning partitions with even parts below odd parts ⋮ On Andrews' integer partitions with even parts below odd parts ⋮ Combinatorics of two second-order mock theta functions

Uses Software

• OEIS

Cites Work

• Partitions associated with the Ramanujan/Watson mock theta functions \(\omega(q)\), \(\nu(q)\) and \(\phi(q)\)
• Partitions, Durfee symbols, and the Atkin-Garvan moments of ranks
• On a calculus of partition functions
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• Applications of Basic Hypergeometric Functions
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