Maximalj-Simplices in the Reald-Dimensional Unit Cube

Large k-D Simplices in the d-Dimensional Cube

Lower bounds for the simplexity of the n-cube

In this paper we prove a new asymptotic lower bound for theminimal number of simplices in simplicial dissections of n-dimensional cubes. In particular we show that the number of simplices in dissections of n-cubes without additional vertices is at least (n + 1) n−1 2 . © 2012 Elsevier B.V. All rights reserved.

LARGEST j-SIMPLICES IN d-CUBES: SOME RELATIVES OF THE HADAMARD MAXIMUM DETERMINANT PROBLEM

This paper studies the computationally diicult problem of nding a largest j-dimensional simplex in a given d-dimensional cube. The case in which j = d is of special interest, for it is equivalent to the Hadamard maximum determinant problem; it has been solved for innnitely many values of d but not for d = 14. (The subcase in which j = d 3 (mod 4) subsumes the famous problem on the existence of ...

Lower Bounds for Simplicial Covers and Triangulations of Cubes

We show that the size of a minimal simplicial cover of a polytope P is a lower bound for the size of a minimal triangulation of P , including ones with extra vertices. We then use this fact to study minimal triangulations of cubes, and we improve lower bounds for covers and triangulations in dimensions 4 through at least 12 (and possibly more dimensions as well). Important ingredients are an an...

Sixteen space-filling curves and traversals for d-dimensional cubes and simplices

This article describes sixteen different ways to traverse d-dimensional space recursively in a way that is well-defined for any number of dimensions. Each of these traversals has distinct properties that may be beneficial for certain applications. Some of the traversals are novel, some have been known in principle but had not been described adequately for any number of dimensions, some of the t...