A Note on John Simplex with Positive Dilation

12/07/2020

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by   Zhou Lu, et al.

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We prove a Johns theorem for simplices in R^d with positive dilation factor d+2, which improves the previously known d^2 upper bound. This bound is tight in view of the d lower bound. Furthermore, we give an example that d isn't the optimal lower bound when d=2. Our results answered both questions regarding Johns theorem for simplices with positive dilation raised by <cit.>.