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Betti numbers and
anti-lecture hall compositions of random threshold graphs
Alexander Engström, Christian Go and Matthew T. Stamps |
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Vol. 319 (2022), No. 1, 75–98
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Abstract |
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We examine 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. |
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Keywords
threshold graphs, Betti numbers, anti-lecture hall
compositions
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Mathematical Subject Classification
Primary: 05A17, 05C25, 05C80, 13D02
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Milestones
Received: 9 September 2021
Revised: 17 April 2022
Accepted: 23 April 2022
Published: 28 August 2022
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Authors |
| Alexander Engström | |
| Department of Mathematics Aalto University Helsinki Finland |
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| Christian Go | |
| Department of Mathematics National University of Singapore Singapore |
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| Matthew T. Stamps | |
| Division of Science Yale-NUS College Singapore |
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