Two-sided Eulerian numbers via balls in boxes
Combinatorics
2012-09-28 v1
Abstract
The Eulerian numbers count permutations according to the number of descents. The two-sided Eulerian numbers count permutations according to number of descents and the number of descents in the inverse permutation. Here we derive some results for Eulerian and two-sided Eulerian numbers using an elementary "balls-in-boxes" approach. We also discuss an open conjecture of Ira Gessel about the two-sided Eulerian numbers.
Cite
@article{arxiv.1209.6273,
title = {Two-sided Eulerian numbers via balls in boxes},
author = {T. Kyle Petersen},
journal= {arXiv preprint arXiv:1209.6273},
year = {2012}
}
Comments
Primarily expository article, to appear in Mathematics Magazine. 23 pages