Vol. 319, No. 1, 2022

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Betti numbers and anti-lecture hall compositions of random threshold graphs

Alexander Engström, Christian Go and Matthew T. Stamps

Vol. 319 (2022), No. 1, 75–98
Abstract

We examine the one-to-one-to-one correspondence between threshold graphs, Betti numbers of quotients of polynomial rings by 2-linear ideals, and anti-lecture hall compositions. In particular, we establish new explicit combinatorial mappings between each of these classes of objects and calculate the expected values of the Betti numbers and anti-lecture hall composition corresponding to a random threshold graph.

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Keywords
threshold graphs, Betti numbers, anti-lecture hall compositions
Mathematical Subject Classification
Primary: 05A17, 05C25, 05C80, 13D02
Milestones
Received: 9 September 2021
Revised: 17 April 2022
Accepted: 23 April 2022
Published: 28 August 2022
Authors
Alexander Engström
Department of Mathematics
Aalto University
Helsinki
Finland
Christian Go
Department of Mathematics
National University of Singapore
Singapore
Matthew T. Stamps
Division of Science
Yale-NUS College
Singapore