Geodesic
Random numerical semigroups and a simplicial complex of irreducible semigroups
Jesus De Loera1 ; Christopher O'Neill2 ; Dane Wilburne3
1University of California Davis
2San Diego State University
3Institute for Computational and Experimental Research in Mathematics
The electronic journal of combinatorics, Tome 25 (2018) no. 4
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We examine properties of random numerical semigroups under a probabilistic model inspired by the Erdos-Renyi model for random graphs. We provide a threshold function for cofiniteness, and bound the expected embedding dimension, genus, and Frobenius number of random semigroups. Our results follow, surprisingly, from the construction of a very natural shellable simplicial complex whose facets are in bijection with irreducible numerical semigroups of a fixed Frobenius number and whose $h$-vector determines the probability that a particular element lies in the semigroup.
DOI : 10.37236/7796
Classification : 20M14, 05E45, 20P05
Mots-clés : threshold function for cofiniteness, bounds for expected embedding dimension, genus, and Frobenius number of random semigroups, shellable simplicial complex

Jesus De Loera  1   ; Christopher O'Neill  2   ; Dane Wilburne  3

1 University of California Davis
2 San Diego State University
3 Institute for Computational and Experimental Research in Mathematics 
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     title = {Random numerical semigroups and a simplicial complex of irreducible semigroups},
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Jesus De Loera; Christopher O'Neill; Dane Wilburne. Random numerical semigroups and a simplicial complex of irreducible semigroups. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/7796

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