Warnaar's bijection and colored partition identities, I

Authors:
Colin Sandon;Fabrizio Zanello
Affiliations:
Department of Mathematics, MIT, Cambridge, MA 02139-4307, United States;Department of Mathematics, MIT, Cambridge, MA 02139-4307, United States and Department of Mathematical Sciences, Michigan Tech, Houghton, MI 49931-1295, United States
Venue:
Journal of Combinatorial Theory Series A
Year:
2013

Citing 3
Cited 0

A generalization of the Farkas and Kra partition theorem for modulus 7

Journal of Combinatorial Theory Series A
Bijective proofs of partition identities arising from modular equations

Journal of Combinatorial Theory Series A
Enumerative Combinatorics: Volume 1

Enumerative Combinatorics: Volume 1

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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. Schroter, 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.