International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 25, Pages 1329-1341
doi:10.1155/S0161171204304114
Counting occurrences of 132 in an even permutation
Department of Mathematics, Chalmers University of Technology, Göteborg 41296, Sweden
Received 9 April 2003
Copyright © 2004 Toufik Mansour. 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 study the generating function for the number of even (or odd)
permutations on n letters containing exactly r≥0 occurrences
of a 132 pattern. It is shown that finding this function for a
given r amounts to a routine check of all permutations in
𝔖2r.