Unboundedness of the first and the last Betti numbers of Numerical Semigroups Generated by Concatenation

TL;DR

This paper demonstrates that certain algebraic invariants, specifically the minimal number of generators and Cohen-Macaulay type, can grow without bound in numerical semigroups formed by concatenating arithmetic sequences.

Contribution

It establishes the unboundedness of key algebraic properties in a specific class of numerical semigroups generated by concatenation.

Findings

Minimal number of generators is unbounded.

Cohen-Macaulay type is unbounded.

Unboundedness applies to Betti numbers of these semigroups.

Abstract

We show that the minimal number of generators and the Cohen-Macaulay type of a family of numerical semigroups generated by concatenation of arithmetic sequences is unbounded.