**Wednesday, 15:15 - 15:40 h, Room: H 2033**

**VĂctor Blanco**

Applications of discrete optimization to numerical semigroups

**Coauthor: Justo Puerto**

**Abstract:**

In this talk we will show some connections between discrete optimization and commutative algebra. In particular we analyze some problems in numerical semigroups, which are sets of nonnegative integers, closed under addition and such that their complement is finite. In this algebraic framework, we will prove that some computations that are usually performed by applying brute force algorithms can be improved by formulating the problems as (single or multiobjective) linear integer programming. For instance, computing the omega invariant of a numerical semigroup (a measure of the primality of the algebraic object), decompositions into irreducible numerical semigroups (special semigroups with simple structure), homogeneus numerical semigroups, or the Kunz-coordinates vector of a numerical semigroups can be done efficiently by formulating the equivalent discrete optimization problem.

Talk 1 of the invited session Wed.3.H 2033

**"Some bridges between algebra and integer programming"** [...]

Cluster 11

**"Integer & mixed-integer programming"** [...]