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On some regular multi-veblen configurations, the geometry of combinatorial quasi Grassmannians

Prażmowska M.

Demonstratio Mathematica

2009

Vol. 42, nr 2

387-402

Multi-Veblen configurations which can be embedded into Desarguesian projective spaces were characterized in [8]: besides the class of combinatorial Grassmannians, only one further class of multi-Veblen configurations shares this property, namely the class of combinatorial quasi Grassmannians introduced in [8]. In this note we discuss relationships between combinatorial Grassmannians and combinatorial quasi Grassmannians, characterize automorphisms of combinatorial quasi Grassmannians, and present some visualizations of them.

Line graphs, their Desarguesian closures, and corresponding groups of automorphisms

Jankowska B., Prażmowska M., Prażmowski K.

Demonstratio Mathematica

2007

Vol. 40, nr 4

971-986

The notion of Desarguesian closure of an arbitrary graph was introduced in [7], and basic properties of Desarguesian closure of complete graphs were also presented in [7]. Then, in [4], the Desarguesian closure of binomial graphs (cf. [5]) was studied. In this paper we shall be mainly concerned with the line graphs associated with complete graphs, their Desarguesian closure, horizon, and automorphisms.

Multiple perspectives and generalizations of the Desargues configuration

Prażmowska M.

Demonstratio Mathematica

2006

Vol. 39, nr 4

887-906

We introduce a class of finite confgurations, which we call combinatorial Grassmannians, and which generalize the Desargues configuration. Fundamental geome- tric properties of them are established, in particular we determine their automorphisms, correlations, mutual embedability, and prove that no one of them contains a Pascal or Pappus figure.

Desarguesian closure of binomial graphs

Klimczak A., Prażmowska M.

Demonstratio Mathematica

2006

Vol. 39, nr 2

245-253

In the paper we study configurations which are obtained as Desarguesian closure of binomial graphs. Their parameters are calculated, and their automorphisms are determined.

A proof of the projective Desargues axiom in the Desarguesian affine plane

Prażmowska M.

Demonstratio Mathematica

2004

Vol. 37, nr 4

921--924

We give a short proof that the projective Desargues axiom is valid in the Desarguesian affine planes.