Counting acyclic and strong digraphs by descents

A descent of a labeled digraph is a directed edge (s,t) with s>t. We count strong tournaments, strong digraphs, acyclic digraphs, and forests by descents and edges. To count strong tournaments we use Eulerian generating functions and to count strong and acyclic digraphs we use a new type of gener...

Full description

Saved in:
Bibliographic Details
Published in:Discrete mathematics 2020-11, Vol.343 (11), p.112041, Article 112041
Main Authors: Archer, Kassie, Gessel, Ira M., Graves, Christina, Liang, Xuming
Format: Article
Language:English
Subjects:
Acyclic digraph
Descent
Eulerian generating function
Graphic generating function
Strong digraph
Strong tournament
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A descent of a labeled digraph is a directed edge (s,t) with s>t. We count strong tournaments, strong digraphs, acyclic digraphs, and forests by descents and edges. To count strong tournaments we use Eulerian generating functions and to count strong and acyclic digraphs we use a new type of generating function that we call a graphic Eulerian generating function.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2020.112041