Split (n + t)-color partitions and 2-color F-partitions

Abstract

Andrews [Generalized Frobenius partitions. Memoirs of the American Math. Soc., 301:1{44, 1984] defined the two classes of generalized F-partitions: F-partitions and k-color F-partitions. For many q-series and Rogers-Ramanujan type identities, the bijections are established between F-partitions and (n + t)-color partitions. Recently (n + t)-color partitions have been extended to split (n+t)-color partitions by Agarwal and Sood [Split (n+t)-color partitions and Gordon-McIntosh eight order mock theta functions. Electron. J. Comb., 21(2):#P2.46, 2014]. The purpose of this paper is to study the k-color F-partitions as a combinatorial tool. The paper includes combinatorial proofs and bijections between split (n + t)-color partitions and 2-color F-partitions for some generalized q-series. Our results further give rise to innate three-way combinatorial identities in conjunction with some Rogers-Ramanujan type identities for some particular cases.