Distribution of descents in matchings

2017/10/11 by Kim, Gene B.
#05A19 #60C05 #60F05 #62E20 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1710.03896

Abstract

The distribution of descents in a fixed conjugacy class of S_n is studied, and it is shown that its moments have an interesting property. A particular conjugacy class that is of interest is the class of matchings (also known as fixed point free involutions). This paper provides a bijective proof of the symmetry of the descents and major indices of matchings and uses a generating function approach to prove an asymptotic normality theorem for the number of descents in matchings.

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