Warnaar's bijection and colored partition identities, I

Details Warnaar's bijection and colored partition identities, I Warnaar's bijection and colored partition identities, I

2011-12-12

arxiv.org/abs/1112.2637v2

Mathematics

Combinatorics

Contains the first portion of the first author's MIT senior thesis (2011). The previous version has now become a two-paper ser

Scientific paper

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. Schroeter, 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.

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