Covering n-Permutations with (n+1)-Permutations
Combinatorics
2012-03-27 v1
Abstract
Let S_n be the set of all permutations on [n]:={1,2,....,n}. We denote by kappa_n the smallest cardinality of a subset A of S_{n+1} that "covers" S_n, in the sense that each pi in S_n may be found as an order-isomorphic subsequence of some pi' in A. What are general upper bounds on kappa_n? If we randomly select nu_n elements of S_{n+1}, when does the probability that they cover S_n transition from 0 to 1? Can we provide a fine-magnification analysis that provides the "probability of coverage" when nu_n is around the level given by the phase transition? In this paper we answer these questions and raise others.
Cite
@article{arxiv.1203.5433,
title = {Covering n-Permutations with (n+1)-Permutations},
author = {Taylor Allison and Anant Godbole and Kathryn Hawley and Bill Kay},
journal= {arXiv preprint arXiv:1203.5433},
year = {2012}
}
Comments
18 pages