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International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 25, Pages 1329-1341
http://dx.doi.org/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 Hindawi Publishing Corporation. 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 r0 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.