Cookies

We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.


Durham Research Online
You are in:

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.

Abstract

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.

Item Type:Article
Full text:PDF - Other (155Kb)
Status:Peer-reviewed
Publisher Web site:http://www.maths.soton.ac.uk/EMIS/journals/EJC/index.html
Record Created:27 Aug 2008
Last Modified:07 Sep 2011 09:52

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitterExport: EndNote, Zotero | BibTex
Usage statisticsLook up in GoogleScholar | Find in a UK Library