New Bounds for Hypercube Slicing Numbers

Abstract : 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.
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Cori, Robert and Mazoyer, Jacques and Morvan, Michel and Mosseri, Rémy. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), pp.155-164, 2001, DMTCS Proceedings
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M. Reza Emamy-Khansary, Martin Ziegler. New Bounds for Hypercube Slicing Numbers. Cori, Robert and Mazoyer, Jacques and Morvan, Michel and Mosseri, Rémy. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), pp.155-164, 2001, DMTCS Proceedings. 〈hal-01182976〉

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