Consider a finite set of vertices. A subset of size d + 1 is called a d-simplex. A chain with coefficients in a field F is a linear combination of oriented d -simplices with coefficients in F. The… (More)

The strong join of two geometries G and H relative to a common subgeometry is a geometry on the point set (G x) u (H x) w x, the closed sets k of which have the property that k n G is closed in the… (More)

Proof. The proof depends on the existence of pairs of orthogonal latin squares of order n = 0 (mod 3), except for n = 6 (see [2, Theorem 13.4.1]). We prove that the lines of K 6 , can be colored in… (More)

Let M be a simple matroid ( = combinatorial geometry). On the bases of M we consider two matroids S(M, F) and H(M, F), which depend on a field F. S(M, F) is the simplicial matroid with coefficients… (More)

A B2-sequence of positive integers a1, a2, ..., ar has the property that the sums ai + aj , 1 ≤ i ≤ j ≤ r, are different. R.C. Bose and S. Chowla have proved the existence of B2-sequences of size r =… (More)