On pythagorean angles
On -clan geometry, .
On rainbowness of semiregular polyhedra
We introduce the rainbowness of a polyhedron as the minimum number such that any colouring of vertices of the polyhedron using at least colours involves a face all vertices of which have different colours. We determine the rainbowness of Platonic solids, prisms, antiprisms and ten Archimedean solids. For the remaining three Archimedean solids this parameter is estimated.
On rank 2 geometries of the Mathieu group .
On Rank 3 Projective Designs.
On rank 4 projective planes.
On rank 5 projective planes.
On rational Morley triangles
On Rusakov’s -ary -groups
Properties of -ary groups connected with the affine geometry are considered. Some conditions for an -ary -group to be derived from a binary group are given. Necessary and sufficient conditions for an -ary group -derived from an additive group of a field to be an -group are obtained. The existence of non-commutative -ary -groups which are not derived from any group of arity for every , is proved.
On S. Gołąb's characterization of the anharmonic ratio
On Schläfli's reduction formula.
On Schur-Ostrowski type theorems for group majorizations.
On sets of vectors of a finite vector space in which every subset of basis size is a basis
It is shown that the maximum size of a set of vectors of a -dimensional vector space over , with the property that every subset of size is a basis, is at most , if , and at most , if , where and is prime. Moreover, for , the sets of maximum size are classified, generalising Beniamino Segre’s “arc is a conic” theorem. These results have various implications. One such implication is that a matrix, with and entries from , has columns which are linearly dependent. Another is...
On small dense sets in Galois planes.
On some flag-transitive non-classical -geometries. II.
On some hyperbolic planes from finite projective planes.
On some properties of a class of geometrical figures.
On some properties of the metric dimension
On Squashed Designs.
On swell-colored complete graphs.