A note on the derived semifield planes of order 16.
A polynomial characterization of affine spaces over GF(3)
A rank 3 tangent complex of , odd.
A recursive construction of 1-rotational Steiner 2-designs.
A study of full collineation group of the projective plane of order 26.
A Sylvester Theorem for Conic Sections.
A theorem of O'Nan for finite linear spaces
A tilde geometry for .
A tropical view on Bruhat-Tits buildings and their compactifications
We relate some features of Bruhat-Tits buildings and their compactifications to tropical geometry. If G is a semisimple group over a suitable non-Archimedean field, the stabilizers of points in the Bruhat-Tits building of G and in some of its compactifications are described by tropical linear algebra. The compactifications we consider arise from algebraic representations of G. We show that the fan which is used to compactify an apartment in this theory is given by the weight polytope of the representation...
A unified construction of finite geometries associated with -clans in characteristic 2.
A universal construction for projective Hjelmslev planes of level
Adjacency preserving mappings.
Affine -structures
Affine regular icosahedron circumscribed around the affine regular octahedron in GS--quasigroup
The concept of the affine regular icosahedron and affine regular octahedron in a general GS-quasigroup will be introduced in this paper. The theorem of the unique determination of the affine regular icosahedron by means of its four vertices which satisfy certain conditions will be proved. The connection between affine regular icosahedron and affine regular octahedron in a general GS-quasigroup will be researched. The geometrical representation of the introduced concepts and relations between them...
Alcuni problemi di ricerca nelle geometrie di Galois
We present a survey on classical problems of Galois geometries. More precisely we discuss some problems and results about ovals, hyperovals, caps, maximal arcs and blocking sets in projective planes and spaces over Galois fields.
Alcuni risultati sui -archi di un piano proiettivo finito
Algebraische Geometrien
Algorithms for Finding Unitals and Maximal Arcs in Projective Planes of Order 16
The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakalo ff , Sofia, July, 2006.Two heuristic algorithms (M65 and M52) for finding respectively unitals and maximal arcs in projective planes of order 16 are described. The exact algorithms based on exhaustive search are impractical because of the combinatorial explosion (huge number of combinations to be checked). Algorithms M65 and M52 use unions of orbits...
All geometries of the Mathieu group based on maximal subgroups.
An alternative definition of the notion valuation in the theory of near polygons.