Forbidden (0, 1)-Vectors in Hyperplanes of Rn: The Restricted Case

Forbidden (0, 1)-vectors in Hyperplanes of Rn: The unrestricted case

‎f‎inding the defining hyperplanes of production possibility set with ‎variable‎ returns to scale using the linear independent ‎vectors‎‎

The Production Possibility Set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs‎. ‎In Data Envelopment Analysis (DEA)‎, ‎it is highly important to identify the defining hyperplanes and especially the strong defining hyperplanes of the empirical PPS‎. ‎Although DEA models can determine the efficiency of a Decision Making Unit (DMU)‎, ‎but they...

A New Proof of the Transposition Theorem

In this note we obtain a formula for the number of orthants intersected by a subspace of R". Stiemke's theorem and ipso the above mentioned transposition theorem will be obtained as a direct consequence of the formula. We employ the following terminology. The hyperplanes Hu • • • , Hs of R" (s 2: n) are said to be in general position if the intersection of any re of them is 0. The ^-dimensional...

Intersection theorems under dimension constraints

In [8] we posed a series of extremal (set system) problems under dimension constraints. In the present paper we study one of them: the intersection problem. The geometrical formulation of our problem is as follows. Given integers 0 ≤ t, k ≤ n determine or estimate the maximum number of (0, 1)–vectors in a k–dimensional subspace of the Euclidean n–space Rn, such that the inner product (“intersec...

Orbits of the hyperoctahedral group as Euclidean designs

The hyperoctahedral group H in n dimensions (the Weyl group of Lie type Bn) is the subgroup of the orthogonal group generated by all transpositions of coordinates and reflections with respect to coordinate hyperplanes. With e1, . . . , en denoting the standard basis vectors of Rn and letting xk = e1 + · · · + ek (k = 1, 2, . . . , n), the set I k = x k = {x k | g ∈ H} is the vertex set of a gen...