Minimal overlapping patterns for generalized Euler permutations, standard tableaux of rectangular shape, and column strict arrays
DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE(2015)
摘要
A permutation tau in the symmetric group S-j is minimally overlapping if any two consecutive occurrences of tau in a permutation sigma can share at most one element. Bona showed that the proportion of minimal overlapping patterns in S-j is at least 3 - e. Given a permutation sigma, we let Des (sigma) denote the set of descents of sigma. We study the class of permutations sigma is an element of S-kn whose descent set is contained in the set {k, 2k, ... (n -1)k}. For example, up-down permutations in S-2n are the set of permutations whose descent equal sigma such that Des (sigma) = {2, 4, ... , 2n - 2}. There are natural analogues of the minimal overlapping permutations for such classes of permutations and we study the proportion of minimal overlapping patterns for each such class. We show that the proportion of minimal overlapping permutations in such classes approaches 1 as k goes to infinity. We also study the proportion of minimal overlapping patterns in standard Young tableaux of shape (n(k)).
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关键词
permutations,arrays,minimal overlapping patterns
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