5 papers
Multiparameter counting of numerical semigroups: recurrences and leaf-discriminating trees
Maria Bras-Amorós, Maria Bras-Amorós, Vicenç Torra +1
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…
Exploring the unleaved tree of numerical semigroups up to a given genus
Maria Bras-Amorós
We present a new algorithm to explore or count the numerical semigroups of a given genus which uses the unleaved version of the tree of numerical semigroups. In the unleaved tree t…
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…
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…