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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 6, Pages 1131–1137
DOI: https://doi.org/10.33048/smzh.2023.64.602 (Mi smj7819) 		 
On the existence of two affine-equivalent frameworks with prescribed edge lengths in Euclidean $d$-space

V. Alexandrovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Physics Department
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DOI: https://doi.org/10.33048/smzh.2023.64.602
Abstract: We study the existence of the two affine-equivalent bar-and-joint frameworks in Euclidean $d$-space which have some prescribed combinatorial structure and edge lengths. We show that the existence problem is always solvable theoretically and explain why to propose a practical algorithm for solving the problem is impossible.
Keywords: Euclidean $d$-space, graph, bar-and-joint framework, affine-equivalent frameworks, Cayley–Menger determinant, Cauchy rigidity theorem.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0006
The research was carried out within the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0006).
Received: 27.06.2023
Revised: 18.09.2023
Accepted: 25.09.2023
English version:
Siberian Mathematical Journal, 2023, Volume 64, Issue 6, Pages 1273–1278
DOI: https://doi.org/10.1134/S0037446623060022
Document Type: Article
UDC: 514.1
Language: Russian
Citation: V. Alexandrov, “On the existence of two affine-equivalent frameworks with prescribed edge lengths in Euclidean $d$-space”, Sibirsk. Mat. Zh., 64:6 (2023), 1131–1137; Siberian Math. J., 64:6 (2023), 1273–1278
Citation in format AMSBIB
\Bibitem{Ale23}
\by V.~Alexandrov
\paper On the existence of two affine-equivalent frameworks with prescribed edge lengths in Euclidean $d$-space
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 6
\pages 1131--1137
\mathnet{http://mi.mathnet.ru/smj7819}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 6
\pages 1273--1278
\crossref{https://doi.org/10.1134/S0037446623060022}
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