Many neighborly spheres

2021/04/09 by Novik, Isabella, Zheng, Hailun · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.04476

Abstract

The result of Padrol asserts that for every d≥ 4, there exist 2^{Ω(nlog 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≥ 5, there are at least 2^Ω(n^{\lfloor (d-1)/2\rfloor}) such types.

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