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Discrete Mathematics & Theoretical Computer Science |
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.
Source : ScholeXplorer
IsRelatedTo ARXIV 1307.1157 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1307.1157
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