TY - JOUR
T1 - On the k-volume rigidity of a simplicial complex in ℝ d
AU - Lew, Alan
AU - Nevo, Eran
AU - Peled, Yuval
AU - Raz, Orit E.
N1 - Publisher Copyright:
© The Author(s), 2025. Published by Cambridge University Press.
PY - 2025/12/5
Y1 - 2025/12/5
N2 - We define a generic rigidity matroid for k-volumes of a simplicial complex in Rd and prove that for 2 ≤ k ≤ d − 1 it has the same rank as the classical generic d-rigidity matroid on the same vertex set (namely, the case k = 1). This is in contrast with the k = d case, previously studied by Lubetzky and Peled, which presents a different behavior. We conjecture a characterization for the bases of this matroid in terms of d-rigidity of the 1-skeleton of the complex and a combinatorial Hall condition on incidences of edges in k-faces.
AB - We define a generic rigidity matroid for k-volumes of a simplicial complex in Rd and prove that for 2 ≤ k ≤ d − 1 it has the same rank as the classical generic d-rigidity matroid on the same vertex set (namely, the case k = 1). This is in contrast with the k = d case, previously studied by Lubetzky and Peled, which presents a different behavior. We conjecture a characterization for the bases of this matroid in terms of d-rigidity of the 1-skeleton of the complex and a combinatorial Hall condition on incidences of edges in k-faces.
UR - https://www.scopus.com/pages/publications/105024129705
U2 - 10.1017/fms.2025.10140
DO - 10.1017/fms.2025.10140
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:105024129705
SN - 2050-5094
VL - 13
JO - Forum of Mathematics, Sigma
JF - Forum of Mathematics, Sigma
M1 - e195
ER -