Geodesic
On the k-volume rigidity of a simplicial complex in Rd
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e195

Voir la notice de l'article provenant de la source Cambridge University Press

We define a generic rigidity matroid for k-volumes of a simplicial complex in $\mathbb {R}^d$ and prove that for $2\leq k \leq d-1$ 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. 
Lew, Alan; Nevo, Eran; Peled, Yuval; Raz, Orit E. On the k-volume rigidity of a simplicial complex in Rd. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e195. doi: 10.1017/fms.2025.10140
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