-configurations with simple edge basis and their corresponding quasigroup identities
There is described a procedure which determines the quasigroup identity corresponding to a given 3-coloured 3-configuration with a simple edge basis.
A construction of resolvable quadruple systems
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 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 note on nonisomorphic Steiner quadruple systems
A note on the realizaiton of distances within sets in euclidean space.
A parallelogram configuration condition in nets
After describing a (general and special) coordinatization of -nets there are found algebraic equivalents for the validity of certain quadrangle configuration conditions in -nets with small degree .
A Recursive Construction for Room Designs
A triangle free configuration
Affine Triple Systems and Matroid Designs.
All 11 3 and 12 3-configurations are rational.
Alon-Babai-Suzuki's conjecture related to binary codes in nonmodular version.
Answer to one of Fishburn's questions: ``Isosceles planar subsets'' [Discrete Comput. Geom. 19 (1998), no. 3, 391--398]
Our short note gives the affirmative answer to one of Fishburn’s questions.
Arranging numbers on circles to reach maximum total variations.
Association schemes. I
Bases of web Configurations
Biembeddings of symmetric configurations and 3-homogeneous Latin trades
Using results of Altshuler and Negami, we present a classification of biembeddings of symmetric configurations of triples in the torus or Klein bottle. We also give an alternative proof of the structure of 3-homogeneous Latin trades.
Binary codes and partial permutation decoding sets from the odd graphs
For k ≥ 1, the odd graph denoted by O(k), is the graph with the vertex-set Ωk, the set of all k-subsets of Ω = 1, 2, …, 2k +1, and any two of its vertices u and v constitute an edge [u, v] if and only if u ∩ v = /0. In this paper the binary code generated by the adjacency matrix of O(k) is studied. The automorphism group of the code is determined, and by identifying a suitable information set, a 2-PD-set of the order of k 4 is determined. Lastly, the relationship between the dual code from O(k)...