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arXiv · 1801.00029

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

Alexander Engström·Christian Go·Matthew T. Stamps
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Abstract

This paper examines 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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Alexander Engström, Christian Go, Matthew T. Stamps. 2021-02-02. Graded Expectations: Betti numbers and anti-lecture hall compositions of random threshold graphs. https://doi.org/10.2140/pjm.2022.319.75

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