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arXiv · 1412.0345

Quadrant Marked Mesh Patterns and the r-Stirling Numbers

Matt Davis
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Abstract

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.

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Matt Davis. 2014-12-01. Quadrant Marked Mesh Patterns and the r-Stirling Numbers. https://arxiv.org/abs/1412.0345

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