Journal of Integer Sequences, Vol. 20 (2017), Article 17.6.3

Width-k Generalizations of Classical Permutation Statistics

Robert Davis
Department of Mathematics
Michigan State University
East Lansing, MI 48824-1027


We introduce new natural generalizations of the classical descent and inversion statistics for permutations, called width-k descents and width-k inversions. These variations induce generalizations of the excedance and major statistics, providing a framework in which well-known equidistributivity results for classical statistics are paralleled. We explore additional relationships among the statistics providing specific formulas in certain special cases. Moreover, we explore the behavior of these width-k statistics in the context of pattern avoidance.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A000108 A001263 A026008 A109446 A166073 A180887 A208343.)

Received January 19 2017; revised version received May 31 2017. Published in Journal of Integer Sequences, June 25 2017.

Return to Journal of Integer Sequences home page