Graded Betti numbers of path ideals of cycles and lines
Ali Alilooee, Sara Faridi
TL;DR
This paper provides a combinatorial formula for all graded Betti numbers of path ideals in line graphs and cycles, simplifying the computation of their algebraic invariants.
Contribution
It introduces a purely combinatorial approach to compute graded Betti numbers of path ideals, offering new proofs for regularity and projective dimension formulas.
Findings
Derived explicit formulas for graded Betti numbers
Simplified proofs for regularity and projective dimension
Enhanced understanding of algebraic properties of path ideals
Abstract
We use purely combinatorial arguments to give a formula to compute all graded Betti numbers of path ideals of line graphs and cycles. As a consequence we can give new and short proofs for the known formulas of regularity and projective dimensions of path ideals of line graphs.
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