Random numerical semigroups and sums of subsets of cyclic groups (2023)
We investigate properties of random numerical semigroups using a probabilistic model based on the Erdös-Rényi model for random graphs and propose a new probabilistic model. We provide a new and more elementary proof of a lower bound of the expected embedding dimension, genus, and Frobenius number of a random semigroup, and provide a tighter probabilistic upper bound. Our results derive from the application of the Probabilistic Method to the generation of random numerical semigroups and observations about sums of uniformly random subsets of cyclic groups. We include experiments that motivated our results.