Many neighborly spheres

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  • Isabella Novik
  • Hailun Zheng

The result of Padrol (Discret Comput Geom 50(4):865–902, 2013) asserts that for every d≥ 4 , there exist 2 Ω(nlogn) distinct combinatorial types of ⌊ d/ 2 ⌋ -neighborly simplicial (d- 1) -spheres with n vertices. We present a construction showing that for every d≥ 5 , there are at least 2Ω(n⌊(d-1)/2⌋) such types.

OriginalsprogEngelsk
TidsskriftMathematische Annalen
Vol/bind388
Sider (fra-til)969–984
ISSN0025-5831
DOI
StatusUdgivet - 2024

Bibliografisk note

Funding Information:
Research of IN is partially supported by NSF grants DMS-1664865 and DMS-1953815, and by Robert R. & Elaine F. Phelps Professorship in Mathematics. Research of HZ is partially supported by a postdoctoral fellowship from ERC grant 716424 - CASe. The authors are grateful to the referee for several clarifying questions.

Funding Information:
Research of IN is partially supported by NSF grants DMS-1664865 and DMS-1953815, and by Robert R. & Elaine F. Phelps Professorship in Mathematics. Research of HZ is partially supported by a postdoctoral fellowship from ERC grant 716424 - CASe.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

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