Covering n-Permutations with (n+1)-Permutations [article]

Taylor Allison, Anant Godbole, Kathryn Hawley, Bill Kay
2012 arXiv   pre-print
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
more » ... _n is around the level given by the phase transition? In this paper we answer these questions and raise others.
arXiv:1203.5433v1 fatcat:2sgzt2rryfctdg5uzhqij4cdo4