Reconstructing simplicial polytopes from their graphs and affine 2-stresses
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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.
Original language | English |
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Journal | Israel Journal of Mathematics |
Volume | 255 |
Pages (from-to) | 891–910 |
ISSN | 0021-2172 |
DOIs | |
Publication status | Published - 2023 |
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© 2022, The Hebrew University of Jerusalem.
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