Quadrant Marked Mesh Patterns and the r-Stirling Numbers
Combinatorics
2014-12-22 v2
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 -Stirling numbers. We examine some ramifications of various properties of the -Stirling numbers for this generating function, and find (seemingly new) formulas for the -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.
Keywords
Cite
@article{arxiv.1412.0345,
title = {Quadrant Marked Mesh Patterns and the r-Stirling Numbers},
author = {Matt Davis},
journal= {arXiv preprint arXiv:1412.0345},
year = {2014}
}
Comments
20 pages v.2: Corrected an out-of-date reference