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Generating function for K-restricted jagged partitions.

Fortin, J-F. and Jacob, P. and Mathieu, P. (2005) 'Generating function for K-restricted jagged partitions.', The electronic journal of combinatorics., 12 (R12). pp. 1-17.


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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Record Created:27 Aug 2008
Last Modified:07 Sep 2011 09:52

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