A graphical way to solve the Boolean matrix equations and
A random walk on the rook placements on a Ferrers board.
A special class of triangular arrays.
Arrangements of Lines with a Minimum Number of Triangles Are Simple.
Asymptotics for the number of -quasigroups of order 4.
Chohomological Aspects of Two-Graphs.
Construction methods for gaussoids
The number of -gaussoids is shown to be a double exponential function in . The necessary bounds are achieved by studying construction methods for gaussoids that rely on prescribing -minors and encoding the resulting combinatorial constraints in a suitable transitive graph. Various special classes of gaussoids arise from restricting the allowed -minors.
Construction of Skew Room Squares.
Dessins d'enfants: bipartite maps and Galois groups.
e-Nets and Simplex Range Queries.
Escher's combinatorial patterns.
Etude sur les plans en blocs incomplets equilibres
Generating random elements of finite distributive lattices.
Génération automatique de mots circulaires et équilibres
Hyperplanes in matroids and the axiom of choice
We show that in set theory without the axiom of choice ZF, the statement sH: “Every proper closed subset of a finitary matroid is the intersection of hyperplanes including it” implies AC, the axiom of choice for (nonempty) finite sets. We also provide an equivalent of the statement AC in terms of “graphic” matroids. Several open questions stay open in ZF, for example: does sH imply the axiom of choice?
Irreduzible Polynome als kombinatorische Figuren.
Isonemality and mononemality of woven fabrics
The paper studies the diagrams of woven fabrics consisting of white and black squares as geometrical objects and described their symmetries. The concepts of isonemality and mononemality due to B. Grünbaum and G. C. Shephard are used. A conjecture of these authors is proved in a particular case.
Latin -parallelepipeds not completing to a Latin cube
Latin parallelepipeds not completing to a cube
Location of polygon vertices on circles and its application in transport studies
The paper deals with the problem how to locate a set of polygon vertices on given circles fulfilling some criteria of "regularity" of individual and composed polygons. Specifying the conditions we can obtain a lot of particular versions of this general problem. Some of them are already solved, the others are not. Applications of this theory can be found in scheduling of periodically repeating processes, e.g. in coordination of several urban lines on a common leg, in optimization of the rhythm of...