2014/02/14 by Jeffrey B. Remmel, Remmel, Jeffrey B., Andrew Timothy Wilson +1 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1402.3358
arxiv created 2014/02/14 · openalex publication_date 2014/02/14 · arxiv updated 2014/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.