Warnaar's bijection and colored partition identities, I
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. 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.
Keywords
Cite
@article{arxiv.1112.2637,
title = {Warnaar's bijection and colored partition identities, I},
author = {Colin Sandon and Fabrizio Zanello},
journal= {arXiv preprint arXiv:1112.2637},
year = {2012}
}
Comments
Contains the first portion of the first author's MIT senior thesis (2011). Some minor revisions with respect to the previous version. To appear in JCTA