Table of Contents
ISRN Combinatorics
Volume 2013, Article ID 806583, 17 pages
http://dx.doi.org/10.1155/2013/806583
Research Article

Generalized Pattern Avoidance Condition for the Wreath Product of Cyclic Groups with Symmetric Groups

1Department of Computer and Information Sceinces, University of Strathclyde Glasgow, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK
2Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA
3Department of Mathematics, University of Wisconsin Eau Claire, Eau Claire, WI 54702-4004, USA

Received 30 September 2012; Accepted 17 October 2012

Academic Editors: Y. Simsek and Y. Zhang

Copyright © 2013 Sergey Kitaev et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We continue the study of the generalized pattern avoidance condition for , the wreath product of the cyclic group with the symmetric group , initiated in the work by Kitaev et al., In press. Among our results, there are a number of (multivariable) generating functions both for consecutive and nonconsecutive patterns, as well as a bijective proof for a new sequence counted by the Catalan numbers.