TY - JOUR

T1 - On the Existence of Two Affine-Equivalent Frameworks with Prescribed Edge Lengths in Euclidean d-Space

AU - Alexandrov, V. A.

N1 - The research was carried out within the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0006).

PY - 2023/11

Y1 - 2023/11

N2 - We study the existence of the two affine-equivalent bar-and-jointframeworks in Euclidean d-space which have some prescribed combinatorialstructure and edge lengths.We show that the existence problem is always solvable theoretically andexplain why to propose a practical algorithm for solving the problem is impossible.

AB - We study the existence of the two affine-equivalent bar-and-jointframeworks in Euclidean d-space which have some prescribed combinatorialstructure and edge lengths.We show that the existence problem is always solvable theoretically andexplain why to propose a practical algorithm for solving the problem is impossible.

KW - 514.1

KW - Cauchy rigidity theorem

KW - Cayley–Menger determinant

KW - Euclidean d-space

KW - affine-equivalent frameworks

KW - bar-and-joint framework

KW - graph

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85178873656&origin=inward&txGid=b6d15ac3cbad263b94dbc1f0dbddee5d

UR - https://www.mendeley.com/catalogue/f9bee595-131d-38d5-a80f-b765180c803f/

U2 - 10.1134/S0037446623060022

DO - 10.1134/S0037446623060022

M3 - Article

VL - 64

SP - 1273

EP - 1278

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 6

ER -