Journal of Integer Sequences, Vol. 27 (2024), Article 24.8.7

Counting Tournaments with a Specified Number of Circular Triads


Ian R. Harris
Department of Statistics and Data Science
Southern Methodist University
Dallas, TX 75214
USA

Ryan P. A. McShane
Department of Statistics
University of Chicago
Chicago, IL 60637
USA

Abstract:

We investigate the counting of tournaments with a specified number of circular triads (3-cycles). We derive the generating functions for the sequences of the counts, and give explicit expressions for the sequences for when the number of circular triads is from 0 through 14.

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(Concerned with sequences A000142 A090672 A357242 A357248 A357257 A357266.)

Received December 14 2023; revised versions received December 15 2023; July 26 2024; December 18 2024. Published in Journal of Integer Sequences, December 18 2024.

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