On lower bounds of the sum of multigraded Betti numbers of simplicial complexes
Li Yu
TL;DR
This paper establishes general lower bounds for the sum of specific multigraded Betti numbers in simplicial complexes with vertex colorings, contributing to the understanding of their algebraic and combinatorial properties.
Contribution
It introduces new lower bounds for multigraded Betti numbers applicable to all simplicial complexes with vertex colorings, advancing algebraic combinatorics.
Findings
Derived general lower bounds for Betti number sums
Applicable to all simplicial complexes with vertex coloring
Enhances understanding of algebraic invariants in combinatorics
Abstract
We find some general lower bounds of the sum of certain families of multigraded Betti numbers of any simplicial complex with a vertex coloring.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Topological and Geometric Data Analysis · Commutative Algebra and Its Applications