Generating function for K-restricted jagged partitions

Details Generating function for K-restricted jagged partitions Generating function for K-restricted jagged partitions

2003-05-26

arxiv.org/abs/math-ph/0305055v3

Electronic J. Comb. 12 (2005) No 1 R12 (17p.)

Physics

Mathematical Physics

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

Scientific paper

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 $n_m\geq 1$ subject to the weakly decreasing conditions $n_i\geq n_{i+1}-1$ and $n_i\geq n_{i+2}$. The $K$-restriction refers to the following additional conditions: $n_i \geq n_{i+K-1} +1$ 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.

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