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December, 2017 The Bressoud-Göllnitz-Gordon Theorem for Overpartitions of Even Moduli
Thomas Yao He, Allison Yi Fang Wang, Alice Xiao Hua Zhao
Taiwanese J. Math. 21(6): 1233-1263 (December, 2017). DOI: 10.11650/tjm/8043

Abstract

We give an overpartition analogue of Bressoud's combinatorial generalization of the Göllnitz-Gordon theorem for even moduli in general case. Let $\widetilde{O}_{k,i}(n)$ be the number of overpartitions of $n$ whose parts satisfy certain difference condition and $\widetilde{P}_{k,i}(n)$ be the number of overpartitions of $n$ whose non-overlined parts satisfy certain congruence condition. We show that $\widetilde{O}_{k,i}(n) = \widetilde{P}_{k,i}(n)$ for $1 \leq i \lt k$.

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Thomas Yao He. Allison Yi Fang Wang. Alice Xiao Hua Zhao. "The Bressoud-Göllnitz-Gordon Theorem for Overpartitions of Even Moduli." Taiwanese J. Math. 21 (6) 1233 - 1263, December, 2017. https://doi.org/10.11650/tjm/8043

Information

Received: 26 December 2016; Revised: 16 March 2017; Accepted: 26 March 2017; Published: December, 2017
First available in Project Euclid: 17 August 2017

zbMATH: 06871367
MathSciNet: MR3732904
Digital Object Identifier: 10.11650/tjm/8043

Subjects:
Primary: 05A17 , 11P84

Keywords: Bailey pair , Göllnitz-Gordon marking , overpartition , the Bressoud-Göllnitz-Gordon theorem

Rights: Copyright © 2017 The Mathematical Society of the Republic of China

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Vol.21 • No. 6 • December, 2017
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