Title

Warnaarʼs bijection and colored partition identities, I

Document Type

Article

Publication Date

1-2013

Abstract

We provide a general and unified combinatorial framework for a number of colored partition identities, which include the five, recently proved analytically by B. Berndt, that correspond to the exceptional modular equations of prime degree due to H. Schröter, R. Russell and S. Ramanujan. Our approach generalizes that of S. Kim, who has given a bijective proof for two of these five identities, namely the ones modulo 7 (also known as the Farkas–Kra identity) and modulo 3. As a consequence of our method, we determine bijective proofs also for the two highly nontrivial identities modulo 5 and 11, thus leaving open combinatorially only the one modulo 23.

Publisher's Statement

© 2012 Elsevier Inc. All rights reserved. Publisher’s version of record: https://doi.org/10.1016/j.jcta.2012.06.008

Publication Title

Journal of Combinatorial Theory, Series A

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