Optimal Betti numbers of forest ideals
Michael Goff
TL;DR
This paper establishes precise bounds on Betti numbers for forest and tree ideals, advancing understanding of their algebraic properties and providing exact limits for specific classes of monomial ideals.
Contribution
It introduces tight bounds on Betti numbers for forest and tree ideals, offering new insights into their algebraic structure.
Findings
Proved a tight lower bound on Betti numbers of tree and forest ideals.
Established a tight upper bound on certain graded Betti numbers of squarefree monomial ideals.
Enhanced understanding of the algebraic invariants of forest and tree ideals.
Abstract
We prove a tight lower bound on the Betti numbers of tree and forest ideals and a tight upper bound on certain graded Betti numbers of squarefree monomial ideals.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic Geometry and Number Theory