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math.CO2026
The shape of a random numerical semigroup
Maria Bras-Amorós, Nathan Kaplan, Deepesh Singhal
We study statistical properties of random numerical semigroups of a given genus. We analyze the graph of a typical numerical semigroup, understood as a function from t…
math.CO2025
Exploring the unleaved tree of numerical semigroups up to a given genus
Maria Bras-Amorós
We present a new algorithm for exploring or counting the numerical semigroups of a given genus that uses the unleaved version of the tree of numerical semigroups. In the unleaved t…
math.CO2024
Greedy Sets and Greedy Numerical Semigroups
Hebert Pérez-Rosés, José Miguel Serradilla-Merinero, Maria Bras-Amorós
Motivated by the change-making problem, we extend the notion of greediness to sets of positive integers not containing the element , and from there to numerical semigroups. We p…