Variations on a Result of Bressoud

Kaǧan Kurşungöz; James A. Sellers

doi:10.1007/s00026-013-0215-4

Variations on a Result of Bressoud

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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.

Original language	English (US)
Pages (from-to)	117-126
Number of pages	10
Journal	Annals of Combinatorics
Volume	18
Issue number	1
DOIs	https://doi.org/10.1007/s00026-013-0215-4
State	Published - Mar 2014
Externally published	Yes

Bibliographical note

Funding Information:
∗J.A. Sellers gratefully acknowledges the support of the Austrian American Educational Commission which supported him during the Summer Semester 2012 as a Fulbright Fellow at the Johannes Kepler University, Linz, Austria.

Keywords

Rogers-Ramanujan-Gordon identities
integer partition

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Variations on a Result of Bressoud

Abstract

Bibliographical note

Keywords

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