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- M. Reza Emamy-Khansary, Martin Ziegler
- DM-CCG
- 2001

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… (More)

- M. Reza Emamy-Khansary
- J. Comb. Theory, Ser. A
- 1986

- M. Reza Emamy-Khansary
- J. Comb. Theory, Ser. A
- 1985

- M. Reza Emamy-Khansary
- INOC
- 2011

- M. Reza Emamy-Khansary, L. Lazarte
- Discrete Mathematics
- 1989

- M. Reza Emamy-Khansary
- Discrete Applied Mathematics
- 1989

In this note, c” is the unit n-cube ((x1,x2, . . . . X,)E W”: Olxir 1, i= 1,2, . . . . n} and the Boolean cube II”= (41)” is the set of vertices of c”. A pseudo-Boolean function is a real-valued function defined on B" [3]. Hammer, Simeone, Liebling and de Werra [4] defined a completely unimodal function (whose class will be denoted by M) as a pseudo-Boolean… (More)

- M. Reza Emamy-Khansary
- CTW
- 2004

- M. Reza Emamy-Khansary, Martin Ziegler
- Discrete Applied Mathematics
- 2008

The cut number S(d) of the d-cube is the minimum number of hyperplanes in R that slice, that is cut the edges while avoiding vertices, all the edges of the d-cube. The cut number problem for the hypercube of dimensions d ≥ 4 was posed by P. O’Neil more than thirty years ago [17]. The identity S(3) = 3 is easy and that of S(4) = 4 is a well-known result, see… (More)

- M. Reza Emamy-Khansary
- Discrete Mathematics
- 1988

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