M. Reza Emamy-Khansary ; Martin Ziegler - New Bounds for Hypercube Slicing Numbers

dmtcs:2296 - Discrete Mathematics & Theoretical Computer Science, January 1, 2001, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001) - https://doi.org/10.46298/dmtcs.2296
New Bounds for Hypercube Slicing Numbers

Authors: M. Reza Emamy-Khansary ; Martin Ziegler

    What is the maximum number of edges of the d-dimensional hypercube, denoted by S(d,k), that can be sliced by k hyperplanes? This question on combinatorial properties of Euclidean geometry arising from linear separability considerations in the theory of Perceptrons has become an issue on its own. We use computational and combinatorial methods to obtain new bounds for S(d,k), d ≤ 8. These strengthen earlier results on hypercube cut numbers.


    Volume: DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001)
    Section: Proceedings
    Published on: January 1, 2001
    Imported on: November 21, 2016
    Keywords: Hypercube cut number,linear separability,combinatorial geometry,[INFO] Computer Science [cs],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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