On the resolution of path ideals of cycles
Ali Alilooee, Sara Faridi
TL;DR
This paper provides formulas and criteria for computing the Betti numbers, projective dimension, and regularity of path ideals of cycles, advancing understanding of their algebraic properties.
Contribution
It introduces a formula for all top degree graded Betti numbers of cycle path ideals and a criterion for their non-zero Betti numbers, along with formulas for projective dimension and regularity.
Findings
Explicit formula for top degree Betti numbers
Criterion for non-zero Betti numbers
Formulas for projective dimension and regularity
Abstract
We give a formula to compute all the top degree graded Betti numbers of the path ideal of a cycle. Also we will find a criterion to determine when Betti numbers of this ideal are non zero and give a formula to compute its projective dimension and regularity.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic Geometry and Number Theory