Combinatorial identities for tenth order mock theta functions

Abstract

In this paper, the open problem posed by Sareen and Rana (Proc. Indian Acad. Sci. (Math. Sci.) 126 (2016) 549–556) is addressed. Here, we interpret two tenth order mock theta functions combinatorially in terms of lattice paths. Then we extend enumeration of one of these with Bender–Knuth matrices; the other by using Frobenius partitions. The combinatorial interpretation of one of these mock theta functions in terms of Frobenius partitions gives an answer to the open problem. Finally, we establish bijections between different classes of combinatorial objects which lead us to one 4-way and one 3-way combinatorial identity.