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

Harvard

Novik, I & Zheng, H 2023, 'Reconstructing simplicial polytopes from their graphs and affine 2-stresses', Israel Journal of Mathematics, vol. 255, pp. 891–910. https://doi.org/10.1007/s11856-022-2459-3

APA

Novik, I., & Zheng, H. (2023). Reconstructing simplicial polytopes from their graphs and affine 2-stresses. Israel Journal of Mathematics, 255, 891–910. https://doi.org/10.1007/s11856-022-2459-3

Vancouver

Novik I, Zheng H. Reconstructing simplicial polytopes from their graphs and affine 2-stresses. Israel Journal of Mathematics. 2023;255:891–910. https://doi.org/10.1007/s11856-022-2459-3

Author

Novik, Isabella ; Zheng, Hailun. / Reconstructing simplicial polytopes from their graphs and affine 2-stresses. In: Israel Journal of Mathematics. 2023 ; Vol. 255. pp. 891–910.

Bibtex

@article{78a9921d93314d7e84b81fc13a2fb83b,
title = "Reconstructing simplicial polytopes from their graphs and affine 2-stresses",
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{\textquoteright}s conjecture holds for the class of k-neighborly polytopes.",
author = "Isabella Novik and Hailun Zheng",
note = "Publisher Copyright: {\textcopyright} 2022, The Hebrew University of Jerusalem.",
year = "2023",
doi = "10.1007/s11856-022-2459-3",
language = "English",
volume = "255",
pages = "891–910",
journal = "Israel Journal of Mathematics",
issn = "0021-2172",
publisher = "Magnes Press",

}

RIS

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