Kagan Kursungoz

Affiliation: Sabanci University

Title Of Talk: a combinatorial construction of Russell's series for CMPP partitions

Abstract: Recently, Capparelli, Meurman, Primc and Primc introduced a class of colored partitions which has since been called CMPP partitions. This generalized earlier work by Primc and S?ikic?. One main reason why CMPP partitions are significant is the authors' conjecture that the generating functions are infinite products in all cases. This question has partially been settled by Dousse and Konan. CMPP partitions are true extensions of the partition classes in the Rogers-Ramanujan-Gordon identities which are defined by difference conditions. As such, a natural question is to look for generating functions similar to the series side of Andrews-Gordon identities. Russell found such bivariate series for one case, and Kanade, Russell, Tsuchioka and Warnaar conjectured another series for another case. Dousse and Konan used representation theory of vertex operator algebras, and Russell used symbolic computation in their proofs. We will combinatorially interpret Russell's bivariate series in a base partition and moves setting.

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