Binomial extensions of Simplicial ideals and reduction number

TL;DR

This paper introduces a new class of binomial ideals linked to simplicial complexes, computes their reduction number, and extends previous results in the study of fiber cones and lattice ideals.

Contribution

It defines binomial extensions of simplicial ideals and provides the first computation of their reduction number, broadening understanding in algebraic combinatorics.

Findings

Computed the reduction number of binomial extensions of simplicial ideals

Extended previous results on fiber cones of lattice ideals

Connected binomial ideals to simplicial complex structures

Abstract

In this article, we define a class of binomial ideals associated to a simplicial complex. This class of ideals appears in the presentation of fiber cones of codimension 2 lattice ideals \cite{hm}, and in the work of Barile and Morales \cite{bm2}, \cite{bm3}, \cite{bm4}. We compute the reduction number of Binomial extensions of Simplicial ideals. This extends all the previous results in this area.