Counting acyclic and strong digraphs by descents

DOI10.1016/j.disc.2020.112041zbMath1452.05073arXiv1909.01550OpenAlexW2971379563MaRDI QIDQ2198383

Ira M. Gessel, Kassie Archer, Christina Graves, Xuming Liang

Publication date: 10 September 2020

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.01550

zbMATH Keywords

descentacyclic digraphstrongly connected digraphstrongly connected tournamentEulerian generating functiongraphic generating function

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Enumeration in graph theory (05C30) Directed graphs (digraphs), tournaments (05C20) Connectivity (05C40)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Chromatic quasisymmetric functions
• A refinement of Cayley's formula for trees
• Bijections for Cayley trees, spanning trees, and their q-analogues
• Counting acyclic digraphs by sources and sinks
• A \(q\)-analog of the exponential formula
• Enumerative applications of a decomposition for graphs and digraphs
• The Tutte polynomial of a graph, depth-first search, and simplicial complex partitions
• Acyclic orientations of graphs
• The Number of k-Coloured Graphs on Labelled Nodes
• Almost all Tournaments are Irreducible
• The Number of Strong Digraphs
• Lagrange inversion