Abstract
A conjecture of Kalai from 1994 posits that for an arbitrary 2 ≤ k ≤ ⌊d/2⌋, the combinatorial type of a simplicial d-polytope P is uniquely determined by the (k − 1)-skeleton of P (given as an abstract simplicial complex) together with the space of affine k-stresses on P. We establish the first non-trivial case of this conjecture, namely, the case of k = 2. We also prove that for a general k, Kalai’s conjecture holds for the class of k-neighborly polytopes.
Originalsprog | Engelsk |
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Tidsskrift | Israel Journal of Mathematics |
Vol/bind | 255 |
Sider (fra-til) | 891–910 |
ISSN | 0021-2172 |
DOI | |
Status | Udgivet - 2023 |
Bibliografisk note
Funding Information:Research of I.N. is partially supported by NSF grants DMS-1664865 and DMS-1953815, and by Robert R. & Elaine F. Phelps Professorship in Mathematics.
Funding Information:
Research of H.Z. is partially supported by a postdoctoral fellowship from ERC grant 716424 — CASe. Acknowledgments
Publisher Copyright:
© 2022, The Hebrew University of Jerusalem.