Year: 2024
Type: article
Abstract: Nevo, Santos, and Wilson constructed $2^{\Omega(N^d)}$ combinatorially distinct simplicial $(2d-1)$-spheres with $N$ vertices. We prove that all spheres produced by one of their methods are shellable. Combining this with prior results of Kalai, Lee, and Benedetti and Ziegler, we conclude that for all $D \ge 3$, there are $2^{\Theta(N^{\lceil D/2 \rceil})}$ shellable simplicial $D$-spheres with $N$ vertices.
DOI: 10.37236/12072
Author: Yirong Yang
Institution: University of Washington
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: National Science Foundation
OpenAlex ID: W4404822377