Freiman ideals

TL;DR

This paper investigates the properties of Freiman ideals, classifying those with maximal height, certain Borel and Hibi ideals, and specific Veronese type ideals, based on the minimal generators of their squares.

Contribution

It provides a classification of Freiman ideals within various classes of monomial ideals, expanding understanding of their algebraic structure and properties.

Findings

Classified all Freiman ideals of maximal height.

Identified Freiman properties in certain Borel and Hibi ideals.

Determined conditions for Veronese type ideals to be Freiman.

Abstract

In this paper we study the Freiman inequality for the minimal number of generators of the square of an equigenerated monomial ideal. Such an ideal is called a Freiman ideal if equality holds in the Freiman inequality. We classify all Freiman ideals of maximal height, the Freiman ideals of certain classes of principal Borel ideals, the Hibi ideals which are Freiman, and classes of Veronese type ideals which are Freiman.