Cyclically consecutive permutation avoidance

2013/12/07 by Richard Ehrenborg, Ehrenborg, Richard
Mathematics · #45C05 #Combinatorics (math.CO) #FOS: Mathematics #Primary 05A05 #math.CO #msc:05A05 #msc:05A15 #msc:45C05 #secondary 05A15

paper · pdf · doi:10.48550/arxiv.1312.2051

6 pages

arxiv created 2013/12/07 · arxiv updated 2013/12/10

Abstract

We give an explicit formula for the number of permutations avoiding cyclically a consecutive pattern in terms of the spectrum of the associated operator of the consecutive pattern. As an example, the number of cyclically consecutive 123-avoiding permutations in \mathfrak S_n is given by n! times the convergent series ∑_k=-∞^∞ ((√(3))/(2π(k+1/3)))ⁿ for n ≥ 2.

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