On the length of the longest subsequence avoiding an arbitrary pattern in a random permutation
组合数学
2007-05-23 v2
摘要
We consider the distribution of the length of the longest subsequence avoiding a given pattern in a random permutation of length n. The well-studied case of a longest increasing subsequence corresponds to avoiding the pattern 21. We show that there is some constant c such that the mean value of this length is asymptotic to twice the square root of c times n and that the distribution of the length is tightly concentrated around its mean. We observe some apparent connections between c and the Stanley-Wilf limit of the class of permutations avoiding the given pattern.
引用
@article{arxiv.math/0505485,
title = {On the length of the longest subsequence avoiding an arbitrary pattern in a random permutation},
author = {Michael H. Albert},
journal= {arXiv preprint arXiv:math/0505485},
year = {2007}
}
备注
14 pages (Reference list corrected)