The Complete Intersection property for binomial ideals of collections of cells

TL;DR

This paper characterizes when inner 2-minor ideals of collections of cells are complete intersections, showing that this occurs precisely when the collection forms a chessboard pattern.

Contribution

It provides a combinatorial criterion, specifically the chessboard structure, for the complete intersection property of binomial ideals associated with collections of cells.

Findings

Inner 2-minor ideal is a complete intersection iff the collection is a chessboard.

Provides a combinatorial characterization linking geometric pattern to algebraic property.

Establishes a clear criterion for algebraic structure based on cell arrangements.

Abstract

In this paper, we provide a combinatorial characterization of those collections of cells whose inner $2$-minor ideals are complete intersections. More precisely, given a collection of cells $\mathcal C$ and its associated inner $2$-minor ideal $I_{\mathcal C}$, we prove that $I_{\mathcal C}$ is a complete intersection if and only if $\mathcal C$ is a chessboard.