Counting acyclic and strong digraphs by descents

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...

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Veröffentlicht in:Discrete mathematics 2020-11, Vol.343 (11), p.112041, Article 112041
Hauptverfasser: Archer, Kassie, Gessel, Ira M., Graves, Christina, Liang, Xuming
Format: Artikel
Sprache:eng
Schlagworte:
Acyclic digraph
Descent
Eulerian generating function
Graphic generating function
Mathematics
Physical Sciences
Science & Technology
Strong digraph
Strong tournament
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Beschreibung
Zusammenfassung: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