Counting Fixed-Length Permutation Patterns
Combinatorics
2012-12-03 v1
Abstract
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 distinct large patterns.
Cite
@article{arxiv.1211.7117,
title = {Counting Fixed-Length Permutation Patterns},
author = {Cheyne Homberger},
journal= {arXiv preprint arXiv:1211.7117},
year = {2012}
}