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Variations on a result of Bressoud

Kurşungöz, Kağan and Sellers, James A. (2014) Variations on a result of Bressoud. Annals of Combinatorics, 18 (1). pp. 117-126. ISSN 0218-0006 (Print) 0219-3094 (Online)

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Official URL: http://dx.doi.org/10.1007/s00026-013-0215-4

Abstract

The well-known Rogers-Ramanujan identities have been a rich source of mathematical study over the last fifty years. In particular, Gordon’s generalization in the early 1960s led to additional work by Andrews and Bressoud in subsequent years. Unfortunately, these results lacked a certain amount of uniformity in terms of combinatorial interpretation. In this work, we provide a single combinatorial interpretation of the series sides of these generating function results by using the concept of cluster parities. This unifies the aforementioned results of Andrews and Bressoud and also allows for a strikingly broader family of q–series results to be obtained. We close the paper by proving congruences for a “degenerate case” of Bressoud’s theorem.

Item Type:Article
Uncontrolled Keywords:integer partition; Rogers-Ramanujan-Gordon identities
Subjects:Q Science > QA Mathematics > QA150-272.5 Algebra
ID Code:25200
Deposited By:Kağan Kurşungöz
Deposited On:02 Dec 2014 21:21
Last Modified:02 Dec 2014 21:21

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