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

DOI: 10.2140/pjm.2022.319.75

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.

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