Width-$k$ Generalizations of Classical Permutation Statistics
Combinatorics
2017-01-18 v1
Abstract
We introduce new natural generalizations of the classical descent and inversion statistics for permutations, called width- descents and width- inversions. These variations induce generalizations of the excedance and major statistics, providing a framework in which the most 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- statistics in the context of pattern avoidance.
Cite
@article{arxiv.1701.04788,
title = {Width-$k$ Generalizations of Classical Permutation Statistics},
author = {Robert Davis},
journal= {arXiv preprint arXiv:1701.04788},
year = {2017}
}
Comments
11 pages