2014/12/01 by Matt Davis, Davis, Matt
Computer Science · Mathematics · #05A05 #05A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1412.0345
openalex publication_date 2014/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Marked mesh patterns are a very general type of permutation pattern. We examine a particular marked mesh pattern originally defined by Kitaev and Remmel, and show that its generating function is described by the r-Stirling numbers. We examine some ramifications of various properties of the r-Stirling numbers for this generating function, and find (seemingly new) formulas for the r-Stirling numbers in terms of the classical Stirling numbers and harmonic numbers. We also answer some questions posed by Kitaev and Remmel and show a connection to another mesh pattern introduced by Kitaev and Liese.