Neighborly spheres and transversal numbers
Isabella Novik, Hailun Zheng
TL;DR
This paper surveys various problems related to the enumeration and properties of neighborly simplicial spheres, including their symmetric variants and associated hypergraph transversal numbers, highlighting both historical and recent developments.
Contribution
It provides a comprehensive overview of open problems and recent advances concerning neighborly simplicial spheres and their transversal hypergraph numbers.
Findings
Summary of known results on the number of simplicial spheres
Discussion of neighborly and centrally symmetric simplicial spheres
Overview of transversal numbers in hypergraphs from simplicial spheres
Abstract
We survey several old and new problems related to the number of simplicial spheres, the number of neighborly simplicial spheres, the number of centrally symmetric simplicial spheres that are cs-neighborly, and the transversal numbers of hypergraphs that arise from simplicial spheres.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Digital Image Processing Techniques · Computational Geometry and Mesh Generation