Paper Info
Title
Alternation acyclic tournaments.
Abstract
We define a tournament to be alternation acyclic if it does not contain a cycle in which descents and ascents alternate. Using a result by Athanasiadis on hyperplane arrangements, we show that these tournaments are counted by the median Genocchi numbers. By establishing a bijection with objects defined by Dumont, we show that alternation acyclic tournaments in which at least one ascent begins at each vertex, except for the largest one, are counted by the Genocchi numbers of the first kind. Unexpected consequences of our results include a pair of ordinary generating function formulas for the Genocchi numbers of both kinds and a simple model for the normalized median Genocchi numbers.
Year
DOI
Venue
2019
10.1016/j.ejc.2019.04.007
European Journal of Combinatorics
DocType
Volume
ISSN
Journal
81
0195-6698
Citations 
PageRank 
References 
0
0.34
0
Authors
1
Name
Order
Citations
PageRank
Gábor Hetyei19619.34