An N-dimensional real representation E of a finite group G is said to have the “Borsuk-Ulam Property” if any continuous G-map from the (N + 1)-fold join of G (an N-complex equipped with the diagonal… (More)

The «-skeleton of a (2« + 2)-simplex does not embed in R " . This well-known result is due (independently) to van Kampen, 1932, and Flores, 1933, who proved the case p = 2 of the following: Theorem.… (More)

A polytope P of 3-space, which meets a given lattice L only in its vertices, is called L-elementary. An L-elementary tetrahedron has volume ≥ (1/6). det(L), in case equality holds it is called… (More)

AN n-dimensional simplicial complex K. n 2 I, which does not embed in R*“, is said to be minimally non-tvd~ddable in W’” if all proper subspaces of the same are embeddable in l&F*“. The well known… (More)

We study the effect of ambient topology on least valences, and so also on the chromatic numbers of embedded simplicial complexes. For example, we prove that a simplicial complex K can be embedded in… (More)

Consider partitions of a cardinality (q ? 1)(d + 1) + 1 generic subset of euclidean d-space, into q parts whose convex hulls have a nonempty intersection. We show that if these partitions are counted… (More)