Fortin, J.-F. and Jacob, P. and Mathieu, P. (2005) 'Generating function for K-restricted jagged partitions.', The electronic journal of combinatorics., 12 . R12.
We present a natural extension of Andrews' multiple sums counting partitions of the form (λ1,⋯,λm) with λi≥λi+k−1+2. The multiple sum that we construct is the generating function for the so-called K-restricted jagged partitions. A jagged partition is a sequence of non-negative integers (n1,n2,⋯,nm) with nm≥1 subject to the weakly decreasing conditions ni≥ni+1−1 and ni≥ni+2. The K-restriction refers to the following additional conditions: ni≥ni+K−1+1 or ni=ni+1−1=ni+K−2+1=ni+K−1. The corresponding generalization of the Rogers-Ramunjan identities is displayed, together with a novel combinatorial interpretation.
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