5 papers
Multiparameter counting of numerical semigroups: recurrences and leaf-discriminating trees
Maria Bras-Amorós, Vicenç Torra
A numerical semigroup is a subset of the nonnegative integers, closed under addition and with finite complement. The size of the complement is its genus. The problem of counting se…
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…
Memory poisoning and secure multi-agent systems
Vicenç Torra, Maria Bras-Amorós
Memory poisoning attacks for Agentic AI and multi-agent systems (MAS) have recently caught attention. It is partially due to the fact that Large Language Models (LLMs) facilitate t…
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…
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…