A Truncated Theta Identity of Gauss and Overpartitions into Odd Parts

Mircea Merca; Chun Wang; Ae Ja Yee

doi:10.1007/s00026-019-00442-x

A Truncated Theta Identity of Gauss and Overpartitions into Odd Parts

Mircea Merca, Chun Wang, Ae Ja Yee

Mathematics

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28 Scopus citations

Abstract

We examine two truncated series derived from a classical theta identity of Gauss. As a consequence, we obtain two infinite families of inequalities for the overpartition function p_o¯ (n) counting the number of overpartitions into odd parts. We provide partition-theoretic interpretations of these results.

Original language	English (US)
Pages (from-to)	907-915
Number of pages	9
Journal	Annals of Combinatorics
Volume	23
Issue number	3-4
DOIs	https://doi.org/10.1007/s00026-019-00442-x
State	Published - Nov 1 2019

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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abstract = "We examine two truncated series derived from a classical theta identity of Gauss. As a consequence, we obtain two infinite families of inequalities for the overpartition function po¯ (n) counting the number of overpartitions into odd parts. We provide partition-theoretic interpretations of these results.",

author = "Mircea Merca and Chun Wang and Yee, {Ae Ja}",

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N2 - We examine two truncated series derived from a classical theta identity of Gauss. As a consequence, we obtain two infinite families of inequalities for the overpartition function po¯ (n) counting the number of overpartitions into odd parts. We provide partition-theoretic interpretations of these results.

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A Truncated Theta Identity of Gauss and Overpartitions into Odd Parts

Abstract

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