New Bounds for Hypercube Slicing Numbers - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2001

New Bounds for Hypercube Slicing Numbers

Martin Ziegler
  • Fonction : Auteur
  • PersonId : 945585

Résumé

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.
Fichier principal
Vignette du fichier
dmAA0111.pdf (107.4 Ko) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-01182976 , version 1 (06-08-2015)

Identifiants

Citer

M. Reza Emamy-Khansary, Martin Ziegler. New Bounds for Hypercube Slicing Numbers. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. pp.155-164, ⟨10.46298/dmtcs.2296⟩. ⟨hal-01182976⟩

Collections

TDS-MACS
64 Consultations
766 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More