Ideals generated by corner-interval minors

TL;DR

This paper investigates binomial ideals generated by corner-interval minors of a generic matrix, determining their minimal primes, radicality, and algebraic properties, with applications to algebraic statistics and contingency tables.

Contribution

It provides a comprehensive analysis of the algebraic structure of ideals generated by corner-interval minors, including minimal primes, radicality, Hilbert-Poincaré polynomial, and regularity formulas.

Findings

Determined minimal prime ideals of the binomial ideals.

Characterized radicality for corner minors.

Computed Hilbert-Poincaré polynomial and regularity formula.

Abstract

In this article, we study binomial ideals generated by an arbitrary collection of corner-interval $2$-minors of a generic matrix. We determine the minimal prime ideals of such ideals and characterize their radicality in the special case of corner minors. Moreover, we discuss connectivity properties of contingency tables in algebraic statistics. We compute the Hilbert-Poincar\'e polynomial of the ideal generated by the set of all corner-interval minors and we derive the formula for the regularity in the case of corner minors.