The Number of k-Cycles In a Family of Restricted Permutations

2017/10/22 by Enes Ozel, Ozel, Enes
Mathematics · #05A05 (Primary) #05A19 (Secondary) #60C05 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #math.CO #math.PR #msc:05A05 #msc:05A19 #msc:60C05

paper · pdf · doi:10.48550/arxiv.1710.07885

17 pages, 1 figure

arxiv created 2018/01/28 · arxiv updated 2018/01/30

Abstract

In this paper we study different restrictions imposed over the set of permutations of size n, S_n, and for specific classes of restrictions study the cycle structure of corresponding permutations. More specifically, we prove that for any fixed positive integer k, the number of k-cycles of a uniformly chosen permutation π∈ S_n with the restriction "π(i) ≥ i-1" for i ∈ \2, …, n\ has a Normal asymptotic distribution. We further prove that this result translates into CLTs regarding multiplicities of fixed-size parts of a uniformly selected composition of n.

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