| author: | M. Reza Emamy-Khansary and Martin Ziegler |
|---|---|
| title: | New Bounds for Hypercube Slicing Numbers |
| keywords: | Hypercube cut number, linear separability, combinatorial geometry |
| 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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| reference: | M. Reza Emamy-Khansary and Martin Ziegler (2001), New Bounds for Hypercube Slicing Numbers, in Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AA, pp. 155-164 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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