Partitions associated with the Ramanujan/Watson mock theta functions ω(q), ν(q)and ϕ(q)

By George E. Andrews, Atul Dixit, A. Yee. 2015

82 citations recorded by the source corpus.

The generating function of partitions with repeated (resp. distinct) parts such that each odd part is less than twice the smallest part is shown to be the third order mock theta function ω(q) (resp. ν(−q)). Similar results for partitions with the corresponding restriction on each even part are also obtained, one of which involves the third order mock theta function ϕ(q). Congruences for the smallest parts partition function(s) associated to such partitions are obtained. Two analogues of the partition-theoretic interpretation of Euler’s pentagonal number theorem are also obtained.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/a82a705b0c49c7bf2f4b171a8cdb289c1a2fc7fd

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

Integer Partitions with Even Parts Below Odd Parts and the Mock Theta Functions (2018, background): “Now the deep combinatorics of ν(−q) have been studied extensively in [6].”