Graded Expectations: Betti numbers and anti-lecture hall compositions of random threshold graphs
arXiv:1801.00029 · doi:10.2140/pjm.2022.319.75
Abstract
This paper examines the one-to-one-to-one correspondence between threshold graphs, Betti numbers of quotients of polynomial rings by -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.
24 pages, 3 figures, and 4 tables