Vol. 319, No. 1, 2022

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 328: 1
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
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.

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