---
_id: '18166'
abstract:
- lang: eng
text: 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.
author:
- first_name: Martin
full_name: Ziegler, Martin
last_name: Ziegler
- first_name: M. Reza
full_name: Emamy-Khansari, M. Reza
last_name: Emamy-Khansari
citation:
ama: '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.'
apa: 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).
bibtex: '@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}
}'
chicago: 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.
ieee: 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.
mla: 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.
short: '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.'
date_created: 2020-08-24T11:29:08Z
date_updated: 2020-08-24T11:29:37Z
department:
- _id: '63'
language:
- iso: eng
page: 155-164
publication: Proceedings of the First International Conference on Discrete Models
- Combinatorics, Computation and Geometry (DM-CCG'2001)
status: public
title: New Bounds for Hypercube Slicing Numbers
type: conference
user_id: '15415'
volume: AA
year: '2001'
...