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Mathematics > Combinatorics

arXiv:1412.0345 (math)
[Submitted on 1 Dec 2014 (v1), last revised 18 Dec 2014 (this version, v2)]

Title:Quadrant Marked Mesh Patterns and the r-Stirling Numbers

Authors: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.
Comments: 20 pages v.2: Corrected an out-of-date reference
Subjects: Combinatorics (math.CO)
MSC classes: 05A05, 05A15
Cite as: arXiv:1412.0345 [math.CO]
  (or arXiv:1412.0345v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1412.0345

Submission history

From: Matt Davis [view email]
[v1] Mon, 1 Dec 2014 04:29:38 UTC (17 KB)
[v2] Thu, 18 Dec 2014 21:24:54 UTC (17 KB)
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