Tangent Cones of Concatenated Numerical Semigroups

TL;DR

This paper investigates the tangent cones and Hilbert series of numerical semigroups formed by concatenating arithmetic sequences, revealing Cohen-Macaulay properties and confirming Rossi's conjecture in specific cases.

Contribution

It introduces a new family of numerical semigroups based on concatenated arithmetic sequences and analyzes their tangent cones and Hilbert series.

Findings

All concatenation classes have Cohen-Macaulay tangent cones except the symmetric class.

The symmetric class satisfies Rossi's conjecture.

Provides structural insights into numerical semigroups formed by concatenation.

Abstract

We study the tangent cone at the origin and the Hilbert series for a family of numerical semigroups generated by concatenation of arithmetic sequences. We prove that all the concatenation classes have Cohen-Macaulay tangent cones except the symmetric class, however, the symmetric class does satisfy Rossi's conjecture.