Quadrant Marked Mesh Patterns
University of Strathclyde
Livingstone Tower, 26 Richmond Street
Glasgow G1 1XH
Department of Mathematics
University of California, San Diego
La Jolla, CA 92093-0112
In this paper we begin the first systematic study of distributions of
quadrant marked mesh patterns. Mesh patterns were introduced recently
by Brändén and Claesson in connection with permutation statistics.
Quadrant marked mesh patterns are based on how many elements lie in
various quadrants of the graph of a permutation relative to the
coordinate system centered at one of the points in the graph of the
permutation. We study the distribution of several quadrant marked mesh
patterns in a symmetric group and in certain subsets of the symmetric
group. We find explicit formulas for the generating function of such
distributions in several general cases and develop recursions to
compute the numbers in question in other cases. In addition, certain
q-analogues of our results are discussed.
Full version: pdf,
(Concerned with sequences
Received January 4 2012;
revised version received April 1 2012.
Published in Journal of Integer Sequences, April 11 2012.
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