Ideals generated by corner-interval minors

2025/06/11 by Nambi, Marie Amalore
#13D40 #13F65 #13F70 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.09618

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-Poincaré 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.

Citations

• On a regularity-conjecture of generalized binomial edge ideals
• Generalized binomial edge ideals of bipartite graphs
• Hilbert series of Parallelogram Polyominoes
• On The Generalized Binomial Edge Ideals of Generalized Block Graphs
• Ideals generated by diagonal 2-minors
• Ideals generated by adjacent 2-minors
• Graphs and Ideals generated by some 2-minors
• Binomial edge ideals and conditional independence statements
• Groebner bases and determinantal ideals
• Binomial Ideals

Related

• Ideals generated by adjacent 2-minors
• Minimal primes and radicality of ideals generated by adjacent 2-minors
• Ideals of Adjacent Minors
• Regularity and depth of binomial ideals arising from combinatorics
• Ideals generated by diagonal 2-minors