Two-sided Eulerian numbers via balls in boxes

2012/09/27 by Petersen, T. Kyle
#05A05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1209.6273

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.

Related

• Generalized Eulerian Numbers
• The Eulerian numbers can D.I.E
• Refined Eulerian numbers and ballot permutations
• Remixed Eulerian numbers: beyond the connected case
• Signed Countings of types B and D permutations and t,q-Euler Numbers