Projective dimension and regularity of path ideals of cycles
Guangjun Zhu
TL;DR
This paper provides formulas to compute the top degree Betti numbers, projective dimension, and regularity of path ideals of cycles, advancing understanding of their algebraic properties.
Contribution
It introduces explicit formulas for Betti numbers, projective dimension, and regularity of path ideals of cycles, which were previously unknown.
Findings
Formulas for top degree Betti numbers of cycle path ideals
Explicit computation of projective dimension and regularity
Enhanced understanding of algebraic invariants of cycle path ideals
Abstract
In this paper, we give a formula to compute all the top degree graded Betti numbers of the path ideals of a cycle. As a consequence we can 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