Taiwanese Journal of Mathematics

The Bressoud-Göllnitz-Gordon Theorem for Overpartitions of Even Moduli

Thomas Yao He, Allison Yi Fang Wang, and Alice Xiao Hua Zhao

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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 $1 \leq i \lt k$.

Article information

Source
Taiwanese J. Math., Volume 21, Number 6 (2017), 1233-1263.

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

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1502935246

Digital Object Identifier
doi:10.11650/tjm/8043

Mathematical Reviews number (MathSciNet)
MR3732904

Zentralblatt MATH identifier
06871367

Subjects
Primary: 05A17: Partitions of integers [See also 11P81, 11P82, 11P83] 11P84: Partition identities; identities of Rogers-Ramanujan type

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

Citation

He, Thomas Yao; Wang, Allison Yi Fang; Zhao, Alice Xiao Hua. The Bressoud-Göllnitz-Gordon Theorem for Overpartitions of Even Moduli. Taiwanese J. Math. 21 (2017), no. 6, 1233--1263. doi:10.11650/tjm/8043. https://projecteuclid.org/euclid.twjm/1502935246


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