Combinatorial proof of a partial theta function identity of Warnaar

Kathy Q. Ji; Byungchan Kim; Jang Soo Kim

doi:10.1142/S1793042116500901

Combinatorial proof of a partial theta function identity of Warnaar

Kathy Q. Ji, Byungchan Kim, Jang Soo Kim

School of Natural Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

By constructing a sign-reversing involution, we prove Warnaar's identity involving a partial theta function, which plays many important roles in the study of asymptotic behaviors and quantum modularities in number theory. We also obtain an Euler-like theorem for a certain kind of unimodal sequences from Warnaar's identity.

Original language	English
Pages (from-to)	1475-1482
Number of pages	8
Journal	International Journal of Number Theory
Volume	12
Issue number	6
DOIs	https://doi.org/10.1142/S1793042116500901
State	Published - 1 Sep 2016

Keywords

combinatorial proof
overpartition
Partial theta function
partition
unimodal sequence
Warnaar's identity

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10.1142/S1793042116500901

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abstract = "By constructing a sign-reversing involution, we prove Warnaar's identity involving a partial theta function, which plays many important roles in the study of asymptotic behaviors and quantum modularities in number theory. We also obtain an Euler-like theorem for a certain kind of unimodal sequences from Warnaar's identity.",

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N2 - By constructing a sign-reversing involution, we prove Warnaar's identity involving a partial theta function, which plays many important roles in the study of asymptotic behaviors and quantum modularities in number theory. We also obtain an Euler-like theorem for a certain kind of unimodal sequences from Warnaar's identity.

AB - By constructing a sign-reversing involution, we prove Warnaar's identity involving a partial theta function, which plays many important roles in the study of asymptotic behaviors and quantum modularities in number theory. We also obtain an Euler-like theorem for a certain kind of unimodal sequences from Warnaar's identity.

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KW - overpartition

KW - Partial theta function

KW - partition

KW - unimodal sequence

KW - Warnaar's identity

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Combinatorial proof of a partial theta function identity of Warnaar

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Keywords

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