Annals of Combinatorics

, Volume 18, Issue 1, pp 117–126 | Cite as

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.

Mathematics Subject Classification

05A17 11P83 

Keywords

integer partition Rogers-Ramanujan-Gordon identities 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Faculty of Engineering and Natural SciencesSabancı UniversityİstanbulTurkey
  2. 2.Department of MathematicsThe Pennsylvania State UniversityState CollegeUSA

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