D-Dimensional Hypercubes and the Euler and MacNeish Conjectures.
Decomposition of complete graphs into -prisms
R. Frucht and J. Gallian (1988) proved that bipartite prisms of order have an -labeling, thus they decompose the complete graph for any positive integer . We use a technique called the -labeling introduced by S. I. El-Zanati, C. Vanden Eynden, and N. Punnim (2001) to show that also some other families of 3-regular bipartite graphs of order called generalized prisms decompose the complete graph for any positive integer .
Decomposition of Convex Figures into Similar Pieces.
Decomposition of special Jacobi sets
Décompositions d'un intervalle réel et des ensembles de Cantor
Defect theorem in the plane
We consider the defect theorem in the context of labelled polyominoes, i.e., two-dimensional figures. The classical version of this property states that if a set of n words is not a code then the words can be expressed as a product of at most n - 1 words, the smaller set being a code. We survey several two-dimensional extensions exhibiting the boundaries where the theorem fails. In particular, we establish the defect property in the case of three dominoes (n × 1 or 1 × n rectangles).
Dělové koule a včelí plásty
Dense packings of equal disks in an equilateral triangle: From 22 to 34 and beyond.
Dense packings of equal spheres in a cube.
Der Darstellungssatz der Allgemeinen Differenzenmethode.
Designs, groups and lattices
The notion of designs in Grassmannian spaces was introduced by the author and R. Coulangeon, G. Nebe, in [3]. After having recalled some basic properties of these objects and the connections with the theory of lattices, we prove that the sequence of Barnes-Wall lattices hold -Grassmannian designs. We also discuss the connections between the notion of Grassmannian design and the notion of design associated with the symmetric space of the totally isotropic subspaces in a binary quadratic space, which...
Dessins d'enfants: bipartite maps and Galois groups.
Determinants of (–1,1)-matrices of the skew-symmetric type: a cocyclic approach
An n by n skew-symmetric type (-1; 1)-matrix K =[ki;j ] has 1’s on the main diagonal and ±1’s elsewhere with ki;j =-kj;i . The largest possible determinant of such a matrix K is an interesting problem. The literature is extensive for n ≡ 0 mod 4 (skew-Hadamard matrices), but for n ≡ 2 mod 4 there are few results known for this question. In this paper we approach this problem constructing cocyclic matrices over the dihedral group of 2t elements, for t odd, which are equivalent to (-1; 1)-matrices...
Determinants of Latin squares of order 8.
Determining the maximal degree of a tree given by its distance matrix
Diagonal similarity of matrices
Dichteste Packungen von gleichen Kreisen in einem Quadrat.
Die Varietät der auflösbaren Ternare der Ordnung 2
Die Zerlegung spezieller Einheitskreisüberdeckungen in drei Einheitskreispackungen
Die Zerlegung von gitterpunktförmigen 2-fachen Einheitskreispackungen in drei Einheitskreispackungen