Path ideals of rooted trees and their graded Betti numbers

2010/08/28 by Rachelle R. Bouchat, Bouchat, Rachelle R., Huy Tài Hà +3
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1008.4829

openalex publication_date 2010/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Γ be a rooted tree and let t be a positive integer. We study algebraic invariants and properties of the path ideal generated by monomial corresponding to paths of length (t-1) in Γ. In particular, we give a recursive formula to compute the graded Betti numbers, a general bound for the regularity, an explicit computation of the linear strand, and we characterize when this path ideal has a linear resolution.

Citations

• Algebraic properties of the path ideal of a tree

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