Path ideals of rooted trees and their graded Betti numbers

Details Path ideals of rooted trees and their graded Betti numbers Path ideals of rooted trees and their graded Betti numbers

2010-08-28

arxiv.org/abs/1008.4829v2

Mathematics

Commutative Algebra

18 pages

Scientific paper

Let $\Gamma$ 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 $\Gamma$. 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.

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