Many neighborly spheres

Autor: Isabella Novik, Hailun Zheng
Rok vydání: 2022
Předmět:
Zdroj: Mathematische Annalen.
ISSN: 1432-1807
0025-5831
DOI: 10.1007/s00208-022-02538-x
Popis: The result of Padrol asserts that for every $d\geq 4$, there exist $2^{\Omega(n\log n)}$ distinct combinatorial types of $\lfloor d/2\rfloor$-neighborly simplicial $(d-1)$-spheres with $n$ vertices. We present a construction showing that for every $d\geq 5$, there are at least $2^{\Omega(n^{\lfloor (d-1)/2\rfloor})}$ such types.
Comment: Rephrased Definition 3.3 and added Definition 3.8; added more details, including proof details, several examples, and an outline of the proof of Theorem 3.1. To appear in Mathematische Annalen
Databáze: OpenAIRE
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