Two way subtable sum problems and quadratic Groebner bases

TL;DR

This paper investigates the algebraic structure of toric ideals from two-way subtable sum problems, showing they have quadratic Groebner bases when subtables are diagonal or triangular, extending previous results on generators.

Contribution

It proves that toric ideals from diagonal or triangular subtables have quadratic Groebner bases, advancing understanding of their algebraic properties.

Findings

Toric ideals from diagonal or triangular subtables possess quadratic Groebner bases.

Quadratic binomials generate these toric ideals under specified conditions.

Extends prior work on generators to Groebner basis properties.

Abstract

Hara, Takemura and Yoshida discuss toric ideals arising from two way subtable sum problems and shows that these toric ideals are generated by quadratic binomials if and only if the subtables are either diagonal or triangular. In the present paper, we show that if the subtables are either diagonal or triangular, then their toric ideals possess quadratic Groebner bases.