New Bounds for Hypercube Slicing Numbers
Emamy-Khansary, M. Reza ; Ziegler, Martin
HAL, hal-01182976 / Harvested from HAL
Text on HAL
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.
Publié le : 2001-07-04
Classification:  Hypercube cut number,  linear separability,  combinatorial geometry,  [INFO]Computer Science [cs],  [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],  [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG],  [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] 
@article{hal-01182976,
     author = {Emamy-Khansary, M. Reza and Ziegler, Martin},
     title = {New Bounds for Hypercube Slicing Numbers},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01182976}
}

Emamy-Khansary, M. Reza; Ziegler, Martin. New Bounds for Hypercube Slicing Numbers. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-01182976/