Abstract
The result of Padrol (Discret Comput Geom 50(4):865–902, 2013) asserts that for every \(d\ge 4\), 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 \(d\ge 5\), there are at least \(2^{\Omega (n^{\lfloor (d-1)/2\rfloor })}\) such types.
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Acknowledgements
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
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.
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