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Journal of Integer Sequences
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 questionsfatcat:7tadvgeyi5hb7fmgarmkdk6p44