Journal of Combinatorics

Volume 6 (2015)

Number 1–2

Block patterns in Stirling permutations

Pages: 179 – 204

DOI: http://dx.doi.org/10.4310/JOC.2015.v6.n1.a10

Authors

Jeffrey B. Remmel (Department of Mathematics, University of California at San Diego)

Andrew Timothy Wilson (Department of Mathematics, University of California at San Diego)

Abstract

We introduce and study a new notion of patterns in Stirling and $k$-Stirling permutations, which we call block patterns. We prove a general result which allows us to compute generating functions for the occurrences of various block patterns in terms of generating functions for the occurrences of patterns in permutations. This result yields a number of applications involving, among other things, Wilf equivalence of block patterns and a new interpretation of Bessel polynomials.We also show how to interpret our results for a certain class of labeled trees, which are in bijection with Stirling permutations.

2010 Mathematics Subject Classification

05A05, 05A15

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