The authors prove upper bounds O((log 1/p)^3) and O((1/p)(log 1/p)^3) for expected embedding dimension and Frobenius number of Erdős-Rényi random numerical semigroups, improving on prior 1/p and 1/p^2 bounds.
40, Springer, Cham, 2020, pp
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Improved Upper Bounds on Key Invariants of Erd\H{o}s-R\'enyi Numerical Semigroups
The authors prove upper bounds O((log 1/p)^3) and O((1/p)(log 1/p)^3) for expected embedding dimension and Frobenius number of Erdős-Rényi random numerical semigroups, improving on prior 1/p and 1/p^2 bounds.