Algebraic properties of universal squarefree lexsegment ideals

TL;DR

This paper investigates the algebraic and combinatorial properties of universal squarefree lexsegment ideals in polynomial rings, exploring their invariants and connections to s-sequences.

Contribution

It introduces new insights into the structure and invariants of universal squarefree lexsegment ideals and their relationship with s-sequences.

Findings

Computed combinatorial invariants of these ideals

Established links between squarefree lexsegment ideals and s-sequences

Provided algebraic characterizations of the ideals

Abstract

Let K be a field and let A be the polynomial ring in n variables with coefficients in the field K We study the universal squarefree lexsegment ideals in A. We put our attention on their combinatorics computing some invariants. Moreover we study the link between such special class of squarefree lexsegment ideals and the so called s-sequences.