Vol. 12, No. 4, 2019

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Descents and des-Wilf equivalence of permutations avoiding certain nonclassical patterns

Caden Bielawa, Robert Davis, Daniel Greeson and Qinhan Zhou

Vol. 12 (2019), No. 4, 549–563
DOI: 10.2140/involve.2019.12.549
Abstract

A frequent topic in the study of pattern avoidance is identifying when two sets of patterns Π,Π are Wilf equivalent, that is, when |Avn(Π)| = |Avn(Π)| for all n. In recent work of Dokos et al. the notion of Wilf equivalence was refined to reflect when avoidance of classical patterns preserves certain statistics. We continue their work by examining des-Wilf equivalence when avoiding certain nonclassical patterns.

Keywords
mesh patterns, pattern avoidance, permutation statistics
Mathematical Subject Classification 2010
Primary: 05A05
Milestones
Received: 23 June 2017
Revised: 25 March 2018
Accepted: 28 October 2018
Published: 16 April 2019

Communicated by Jim Haglund
Authors
Caden Bielawa
Department of Mathematics
Michigan State University
East Lansing, MI
United States
Robert Davis
Department of Mathematics
Michigan State University
East Lansing, MI
United States
Daniel Greeson
Department of Mathematics
Michigan State University
East Lansing, MI
United States
Qinhan Zhou
School of Mathematics and Statistics
Xi’an Jiaotong University
Xi’an, Shaanxi
China