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Generating function for K-restricted jagged partitions

Fortin, Jean-Francois; Jacob, Patrick; Mathieu, Pierre

Authors

Jean-Francois Fortin

Patrick Jacob

Pierre Mathieu



Abstract

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.

Citation

Fortin, J., Jacob, P., & Mathieu, P. (2005). Generating function for K-restricted jagged partitions. Electronic Journal of Combinatorics, 12,

Journal Article Type Article
Publication Date Feb 21, 2005
Deposit Date Aug 27, 2008
Publicly Available Date Aug 27, 2008
Journal Electronic Journal of Combinatorics
Publisher Electronic Journal of Combinatorics
Peer Reviewed Peer Reviewed
Volume 12
Publisher URL http://www.maths.soton.ac.uk/EMIS/journals/EJC/ojs/index.php/eljc/article/view/v12i1r12
Related Public URLs http://arxiv.org/abs/math-ph/0305055

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