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arXiv · 1203.5433

Covering n-Permutations with (n+1)-Permutations

Taylor Allison·Anant Godbole·Kathryn Hawley·Bill Kay
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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.

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Taylor Allison, Anant Godbole, Kathryn Hawley, Bill Kay. 2012-03-24. Covering n-Permutations with (n+1)-Permutations. https://arxiv.org/abs/1203.5433

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