%0 Journal Article
%T Counting Fixed-Length Permutation Patterns
%A Cheyne Homberger
%J Online Journal of Analytic Combinatorics
%D 2012
%I University of Auckland
%X We consider the problem of packing fixed-length patterns into a permutation, and develop a connection between the number of large patterns and the number of bonds in a permutation. Improving upon a result of Kaplansky and Wolfowitz, we obtain exact values for the expectation and variance for the number of large patterns in a random permutation. Finally, we are able to generalize the idea of bonds to obtain results on fixed-length patterns of any size, and present a construction that maximizes the number of patterns of a fixed size.
%U http://analytic-combinatorics.org/index.php/ojac/article/view/36