Reconstructing simplicial polytopes from their graphs and affine 2-stresses
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Reconstructing simplicial polytopes from their graphs and affine 2-stresses. / Novik, Isabella; Zheng, Hailun.
In: Israel Journal of Mathematics, Vol. 255, 2023, p. 891–910.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Reconstructing simplicial polytopes from their graphs and affine 2-stresses
AU - Novik, Isabella
AU - Zheng, Hailun
N1 - Publisher Copyright: © 2022, The Hebrew University of Jerusalem.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
U2 - 10.1007/s11856-022-2459-3
DO - 10.1007/s11856-022-2459-3
M3 - Journal article
AN - SCOPUS:85136279592
VL - 255
SP - 891
EP - 910
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
SN - 0021-2172
ER -
ID: 344728437