High-Dimensional Centrally Symmetric Polytopes with Neighborliness Proportional to Dimension

  title={High-Dimensional Centrally Symmetric Polytopes with Neighborliness Proportional to Dimension},
  author={David L. Donoho},
  journal={Discrete & Computational Geometry},
Let A be a d by n matrix, d < n. Let C be the regular cross polytope (octahedron) in R. It has recently been shown that properties of the centrosymmetric polytope P = AC are of interest for finding sparse solutions to the underdetermined system of equations y = Ax; [9]. In particular, it is valuable to know that P is centrally k-neighborly. We study the face numbers of randomly-projected cross-polytopes in the proportionaldimensional case where d ∼ δn, where the projector A is chosen uniformly… CONTINUE READING
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