A construction method for generalized Room squares. (Short Communication).
A construction of resolvable quadruple systems
A determinant formula from random walks
One usually studies the random walk model of a cat moving from one room to another in an apartment. Imagine now that the cat also has the possibility to go from one apartment to another by crossing some corridors, or even from one building to another. That yields a new probabilistic model for which each corridor connects the entrance rooms of several apartments. This article computes the determinant of the stochastic matrix associated to such random walks. That new model naturally allows to compute...
A discrete Fourier kernel and Fraenkel's tiling conjecture
A family of 4-designs on 26 points
Using the Kramer-Mesner method, - designs with as a group of automorphisms and with in the set are constructed. The search uses specific partitioning of columns of the orbit incidence matrix, related to so-called “quasi-designs”. Actions of groups , and twisted are being compared. It is shown that there exist - designs with , respectively twisted as a group of automorphisms and with in the set . With in the set , there exist designs which possess all three considered groups...
A family of complete arcs in finite projective planes
A few more cyclic Steiner 2-designs.
A forbidden-suborder characterization of binarily-composable diagrams in double categories.
A further look into combinatorial orthogonality.
A generalization of group difference sets and the matrix equation Am = dI + ...J.
A generalization of transversals for Latin squares.
A Generalized Mean-Value Theorem.
A geometric approach to universal quasigroup identities
In the present paper we construct the accompanying identity of a given quasigroup identity . After that we deduce the main result: is isotopically invariant (i.e., for every guasigroup it holds that if is satisfied in then is satisfied in every quasigroup isotopic to ) if and only if it is equivalent to (i.e., for every quasigroup it holds that in either are both satisfied or both not).
A Geometric Characterization of Moufang Hexagons.
A geometric theory of hypergraph colouring.
A Gessel--Viennot-type method for cycle systems in a directed graph.
A graphical way to solve the Boolean matrix equations and
A Hajós type result on factoring finite abelian groups by subsets. II
It is proved that if a finite abelian group is factored into a direct product of lacunary cyclic subsets, then at least one of the factors must be periodic. This result generalizes Hajós's factorization theorem.
A local minimum energy condition of hexagonal circle packing.
A Matroid on Hypergraphs, with Applications in Scene Analysis and Geometry.