Rights statement: First Published in SIAM Journal on Discrete Mathematics in 35 (2), 2021published by the Society for Industrial and Applied Mathematics (SIAM) Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
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TY - JOUR
T1 - An improved bound for the rigidity of linearly constrained frameworks
AU - Jackson, Bill
AU - Nixon, Anthony
AU - Tanigawa, Shin-Ichi
N1 - First Published in SIAM Journal on Discrete Mathematics in 35 (2), 2021published by the Society for Industrial and Applied Mathematics (SIAM) Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
PY - 2021/5/4
Y1 - 2021/5/4
N2 - We consider the problem of characterising the generic rigidity of bar-jointframeworks in Rdin which each vertex is constrained to lie in a given affine subspace.The special case when d = 2 was previously solved by I. Streinu and L. Theran in 2010and the case when each vertex is constrained to lie in an affine subspace of dimension t,and d ≥ t(t − 1) was solved by Cruickshank, Guler and the first two authors in 2019. Weextend the latter result by showing that the given characterisation holds whenever d ≥ 2t.
AB - We consider the problem of characterising the generic rigidity of bar-jointframeworks in Rdin which each vertex is constrained to lie in a given affine subspace.The special case when d = 2 was previously solved by I. Streinu and L. Theran in 2010and the case when each vertex is constrained to lie in an affine subspace of dimension t,and d ≥ t(t − 1) was solved by Cruickshank, Guler and the first two authors in 2019. Weextend the latter result by showing that the given characterisation holds whenever d ≥ 2t.
KW - rigidity
KW - linearly constrained framework
KW - pinned framework
KW - count matroid
U2 - 10.1137/20M134304X
DO - 10.1137/20M134304X
M3 - Journal article
VL - 35
SP - 928
EP - 933
JO - SIAM Journal on Discrete Mathematics
JF - SIAM Journal on Discrete Mathematics
SN - 0895-4801
IS - 2
ER -