Generating function for K-restricted jagged partitions

Abstract

We present a natural extension of Andrews' multiple sums counting partitions with difference 2 at distance $k-1$, by deriving the generating function for $K$-restricted jagged partitions. A jagged partition is a collection of non-negative integers $(n_1,n_2,...,n_m)$ with $n_m\ge 1$ subject to the weakly decreasing conditions $n_i\ge n_{i+1}-1$ and $n_i\ge n_{i+2}$. The $K$-restriction refers to the following additional conditions: $n_i\ge n_{i+K-1}+1$ or $n_i=n_{i+1}-1=n_{i+K-2}+1=n_{i+K-1}$. The corresponding generalization of the Rogers-Ramunjan identities is displayed, together with a novel combinatorial interpretation.

latex, 13 pages; minor modifications and one more section (6) added

References in corpus (1)

• Particle content of the (k,3)-configurations