Biplanes.
Characterisation of some sparse binary sequential arrays.
Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths
Dedicated to the memory of the late professor Stefan Dodunekov on the occasion of his 70th anniversary. We classify up to multiplier equivalence maximal (v, 3, 1) optical orthogonal codes (OOCs) with v ≤ 61 and maximal (v, 3, 2, 1) OOCs with v ≤ 99. There is a one-to-one correspondence between maximal (v, 3, 1) OOCs, maximal cyclic binary constant weight codes of weight 3 and minimum dis tance 4, (v, 3; ⌊(v − 1)/6⌋) difference packings, and maximal (v, 3, 1) binary cyclically permutable constant...
Cliques and Claws in Edge-transitive Strongly Regular Graphs.
Closure conditions of commutativity
There are investigated some closure conditions of Thomsen type in 3-webs which gurantee that at least one of coordinatizing quasigroups of a given 3-web is commutative.
Coherent configurations I
Combinatorial lemmas for polyhedrons
We formulate general boundary conditions for a labelling to assure the existence of a balanced n-simplex in a triangulated polyhedron. Furthermore we prove a Knaster-Kuratowski-Mazurkiewicz type theorem for polyhedrons and generalize some theorems of Ichiishi and Idzik. We also formulate a necessary condition for a continuous function defined on a polyhedron to be an onto function.
Combinatorial lemmas for polyhedrons I
We formulate general boundary conditions for a labelling of vertices of a triangulation of a polyhedron by vectors to assure the existence of a balanced simplex. The condition is not for each vertex separately, but for a set of vertices of each boundary simplex. This allows us to formulate a theorem, which is more general than the Sperner lemma and theorems of Shapley; Idzik and Junosza-Szaniawski; van der Laan, Talman and Yang. A generalization of the Poincaré-Miranda theorem is also derived.
Combinatorial Structures in Loops.
Conditions nécessaires d’existence des -plans
Les -plans (définis ci-dessous) ont été introduits dans [1]. Leur étude englobe celle des plans affines et projectifs finis, des familles de carrés latins deux à deux orthogonaux, de certains plans équilibrés et partiellement équilibrés . La question de leur existence est très mal connue, celle de leur unicité n’a pratiquement pas été abordée. Nous nous proposons de montrer le théorème suivant : pour qu’il existe un -plan il est nécessaire que : soient entiers.
Configuration of mutually perspective triangles
Configurations of rank- extremal even unimodular lattices ()
We show that if is an extremal even unimodular lattice of rank with , then is generated by its vectors of norms and . Our result is an extension of Ozeki’s result for the case .
Conjugate cyclic -configurations
Constructing 5-configurations with chiral symmetry.
Construction of Skew Room Squares.
Construction of solvable near-block designs with the aid of a computer. (Konstruktion auflösbarer Fast-Blockpläne mit Hilfe eines Computers.)
Construction, properties and applications of finite neofields
We give a short account of the construction and properties of left neofields. Most useful in practice seem to be neofields based on the cyclic group and particularly those having an additional divisibility property, called D-neofields. We shall give examples of applications to the construction of orthogonal latin squares, to the design of tournaments balanced for residual effects and to cryptography.
Constructions of color schemes
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 .