Quadrant Marked Mesh Patterns and the r-Stirling Numbers
Department of Mathematics and Computer Science
163 Stormont St.
New Concord, OH 43762
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.
Full version: pdf,
(Concerned with sequences
Received November 30 2014;
revised versions received April 12 2015; August 31 2015.
Published in Journal of Integer Sequences, September 8 2015.
Journal of Integer Sequences home page