Counting acyclic and strong digraphs by descents
Combinatorics
2020-08-10 v3
Abstract
A descent of a labeled digraph is a directed edge (s, t) with s > t. We count strong tournaments, strong digraphs, and acyclic digraphs 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.
Keywords
Cite
@article{arxiv.1909.01550,
title = {Counting acyclic and strong digraphs by descents},
author = {Kassie Archer and Ira M. Gessel and Christina Graves and Xuming Liang},
journal= {arXiv preprint arXiv:1909.01550},
year = {2020}
}
Comments
23 pages. Fixed typo