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2017 Some connections between permutation cycles and Touchard polynomials and between permutations that fix a set and covers of multisets
Ross G. Pinsky
Electron. Commun. Probab. 22: 1-9 (2017). DOI: 10.1214/17-ECP49

Abstract

We present a new proof of a fundamental result concerning cycles of random permutations which gives some intuition for the connection between Touchard polynomials and the Poisson distribution. We also introduce a rather novel permutation statistic and study its distribution. This quantity, indexed by $m$, is the number of sets of size $m$ fixed by the permutation. This leads to a new and simpler derivation of the exponential generating function for the number of covers of certain multisets.

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Ross G. Pinsky. "Some connections between permutation cycles and Touchard polynomials and between permutations that fix a set and covers of multisets." Electron. Commun. Probab. 22 1 - 9, 2017. https://doi.org/10.1214/17-ECP49

Information

Received: 30 January 2017; Accepted: 14 February 2017; Published: 2017
First available in Project Euclid: 18 February 2017

zbMATH: 06691236
MathSciNet: MR3615668
Digital Object Identifier: 10.1214/17-ECP49

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JOURNAL ARTICLE
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