On Simplicial Complexes with Extremal Total Betti number and Total Bigraded Betti Number
Pimeng Dai, Li Yu
TL;DR
This paper characterizes simplicial complexes that maximize or minimize the total Betti and bigraded Betti numbers for a fixed number of vertices across dimensions, providing insights into their topological complexity.
Contribution
It identifies the extremal simplicial complexes with respect to total and bigraded Betti numbers given a fixed number of vertices in each dimension.
Findings
Determined complexes with maximum total Betti number.
Identified complexes with minimum total Betti number.
Analyzed extremal properties of bigraded Betti numbers.
Abstract
We determine which simplicial complexes have the maximum or minimum sum of Betti numbers and sum of bigraded Betti numbers with a given number of vertices in each dimension.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Commutative Algebra and Its Applications · Advanced Combinatorial Mathematics