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Paata Ivanishvili
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Let $\gamma :[0,1] \mapsto \mathbb{R}^{n}$ be a curve such that all the leading principal minors of the matrix $(\gamma^{(1)}(t), \ldots, \gamma^{(n)}(t))$ are nonvanishing as $t \in [0,1]$.

Theorem: the minimal number $k$ points required to represent any interior point of $\mathrm{Conv}(\gamma([0,1]))$ as a convex combination of $k$ points of $\gamma([0,1])$ equals $\lfloor \frac{n}{2}\rfloor+1$.

Paata Ivanishvili
  • 3.9k
  • 1
  • 21
  • 30