The paper establishes non-trivial dimensional thresholds for volume vectors determined by hypergraphs of simplices via a Jacobian method leveraging distance results and a refinement for planar triangles, improving prior bounds.
Euclidean dis- tance geometry and applications
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On volume vectors determined by hypergraphs in thin subsets of Euclidean space
The paper establishes non-trivial dimensional thresholds for volume vectors determined by hypergraphs of simplices via a Jacobian method leveraging distance results and a refinement for planar triangles, improving prior bounds.