Frobenius partition theoretic interpretations of some basic series identities

Using generalized Frobenius partitions we interpret five basic series identities of Rogers combinatorially.  This extends the recent work of Goyal and Agarwal and yields five new 3-way combinatorial identities

New combinatorial interpretations of some Rogers-Ramanujan type identities

In present paper, three Rogers-Ramanujan type identities are interpreted combinatorially in terms of certain associated lattice path functions. Out of these three identities, two are further explored using the Bender-Knuth matrices. These results give new combinatorial interpretations of these basic series identities. Using a bijection between the associated lattice path functions and the ($n+t$)-color partitions and that of between the associated lattice path functions and the weighted lattice path functions, we extend the recent work of Sareen and Rana to three new 5-way combinatorial identities. By using the bijection between Bender-Knuth matrices and the $n$-color partitions, we further extend their work to two new 6-way combinatorial identities

On a generalized basic series and Rogers–Ramanujan type identities - II

This paper is in continuation with our recent paper “On a generalized basic series and Rogers-Ramanujan type identities”. Here, we consider two generalized basic series and interpret these basic series as the generating function of some restricted $(n + t)$-color partitions and restricted weighted lattice paths. The basic series discussed in the aforementioned paper, is now a mere particular case of one of the generalized basic series that are discussed in this paper. Besides, eight particular cases are also discussed which give combinatorial interpretations of eight Rogers–Ramanujan type identities which are combinatorially unexplored till date

On combinatorial extensions of Rogers-Ramanujan type identities

In the present paper we use anti-hook differences of Agarwal and Andrews as an elementary tool to provide new partition theoretic meanings to two generalized basic series in terms of ordinary partitions satisfying certain anti-hook difference conditions. Five particular cases are also discussed. These particular cases yield new partition theoretic versions of G\"{o}llnitz-Gordon identities and G\"{o}llnitz identity. Five $q$-identities of Rogers and three $q$-identities of Slater are further explored. These results extend the work of Goyal and Agarwal, Agarwal and Rana and Sareen and Rana

Some Separable integer partition classes

Recently, Andrews introduced separable integer partition classes and analyzed some well-known theorems. In this paper, we investigate partitions with parts separated by parity introduced by Andrews with the aid of separable integer partition classes with modulus $2$. We also extend separable integer partition classes with modulus $1$ to overpartitions, called separable overpartition classes. We study overpartitions and the overpartition analogue of Rogers-Ramanujan identities, which are separable overpartition classes

A new approach and generalizations to some results about mock theta functions

AbstractSome mock theta functions have been interpreted in terms of n-color partition. In this paper we use a new technique to gain a deeper insight on these interpretations, as well as we employ this new technique to obtain in a more systematic way similar new interpretations for three other mock theta functions