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
USA

Abstract:

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.


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(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.


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