Almost reverse lexicographic ideals and Fr\"{o}berg sequence

TL;DR

This paper characterizes almost reverse lexicographic ideals in polynomial rings and demonstrates that all Fröberg sequences can be realized as Hilbert functions of such ideals, providing a new criterion for these sequences.

Contribution

It introduces a criterion for sequences to be Hilbert functions of almost reverse lexicographic ideals and proves all Fröberg sequences meet this criterion.

Findings

Fröberg sequences satisfy the new criterion.

A characterization criterion for almost reverse lexicographic ideals.

Connection established between Fröberg sequences and these ideals.

Abstract

We study almost reverse lexicographic ideals in a polynomial ring over a field of arbitrary characteristic. We give a criterion for a given sequence of nonnegative integers to be the Hilbert function of an almost reverse lexicographic ideal in the polynomial ring. Then it will be shown that every Fr\"{o}berg sequence satisfies this criterion.