New Bounds for Hypercube Slicing Numbers
M. Ziegler, M.R. Emamy-Khansari, in: Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001), 2001, pp. 155–164.
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Conference Paper
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Author
Ziegler, Martin;
Emamy-Khansari, M. Reza
Abstract
What is the maximum number of edges of the d-dimensional hypercube, denoted by S(d,k), that can be sliced by k many 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 on S(d,k), s<=8. These strengthen earlier results on hypercube cut numbers.
Publishing Year
Proceedings Title
Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG'2001)
Volume
AA
Page
155-164
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Ziegler M, Emamy-Khansari MR. New Bounds for Hypercube Slicing Numbers. In: Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001). Vol AA. ; 2001:155-164.
Ziegler, M., & Emamy-Khansari, M. R. (2001). New Bounds for Hypercube Slicing Numbers. In Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001) (Vol. AA, pp. 155–164).
@inproceedings{Ziegler_Emamy-Khansari_2001, title={New Bounds for Hypercube Slicing Numbers}, volume={AA}, booktitle={Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001)}, author={Ziegler, Martin and Emamy-Khansari, M. Reza}, year={2001}, pages={155–164} }
Ziegler, Martin, and M. Reza Emamy-Khansari. “New Bounds for Hypercube Slicing Numbers.” In Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001), AA:155–64, 2001.
M. Ziegler and M. R. Emamy-Khansari, “New Bounds for Hypercube Slicing Numbers,” in Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001), 2001, vol. AA, pp. 155–164.
Ziegler, Martin, and M. Reza Emamy-Khansari. “New Bounds for Hypercube Slicing Numbers.” Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001), vol. AA, 2001, pp. 155–64.
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