Path ideals of rooted trees and their graded Betti numbers |
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| Authors: | Rachelle R Bouchat Huy Tài Hà Augustine O?Keefe |
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| Institution: | a Department of Mathematics, Slippery Rock University, 1 Morrow Way, Slippery Rock, PA 16057, United States
b Department of Mathematics, Tulane University, 6823 St. Charles Ave., New Orleans, LA 70118, United States |
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| Abstract: | Let Γ be a rooted (and directed) tree, and let t be a positive integer. The path ideal It(Γ) is generated by monomials that correspond to directed paths of length (t−1) in Γ. In this paper, we study algebraic properties and invariants of It(Γ). We give a recursive formula to compute the graded Betti numbers of It(Γ) in terms of path ideals of subtrees. We also give a general bound for the regularity, explicitly compute the linear strand, and investigate when It(Γ) has a linear resolution. |
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| Keywords: | Edge ideals Path ideals Regularity Minimal free resolution |
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