conference paper
New Bounds for Hypercube Slicing Numbers
Martin
Ziegler
author
M. Reza
Emamy-Khansari
author
63
department
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.
2001
eng
Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG'2001)
AA155-164
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.
@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 <i>Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001)</i>, AA:155–64, 2001.
M. Ziegler and M. R. Emamy-Khansari, “New Bounds for Hypercube Slicing Numbers,” in <i>Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001)</i>, 2001, vol. AA, pp. 155–164.
Ziegler, Martin, and M. Reza Emamy-Khansari. “New Bounds for Hypercube Slicing Numbers.” <i>Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001)</i>, vol. AA, 2001, pp. 155–64.
Ziegler, M., & Emamy-Khansari, M. R. (2001). New Bounds for Hypercube Slicing Numbers. In <i>Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001)</i> (Vol. AA, pp. 155–164).
Ziegler M, Emamy-Khansari MR. New Bounds for Hypercube Slicing Numbers. In: <i>Proceedings of the First International Conference on Discrete Models - Combinatorics, Computation and Geometry (DM-CCG’2001)</i>. Vol AA. ; 2001:155-164.
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