Generating function for K-restricted jagged partitions

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

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
• Public URL: https://durham-repository.worktribe.com/output/1570404
• 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