arXiv subjects
Publications and source records attributed to Krzysztof Prażmowski.
A combinatorial object representing schemas of, possibly skew, perspectives, called {\em a configuration of skew perspective} has been defined in \cite{klik:binom}, \cite{maszko}. Here we develop the theory of configurations generalizing perspectives defined in combinatorial Veronesians. The complete classification of thus obtained $({15}_4 {20}_3)$-configurations is presented.
An elegant procedure which characterizes a decomposition of some class of binomial configurations into two other, resembling a definition of Pascal's Triangle, was given in \cite{gevay}. In essence, this construction was already presented in \cite{perspect}. We show that such a procedure is a result of fixing in configurations in some class $\mathcal K$ suitable hyperplanes which both: are in this class, and deleting such a hyperplane results in a configuration in this class. By a way of example we show two more (added to that of \cite{gevay}) natural classes of such configurations, discuss some other, and propose some open questions that seem also natural in this context.
A combinatorial object representing schemas of, possibly skew, perspectives, called {\em a configuration of skew perspective} is defined. Some classifications of skew perspectives are presented.
In the paper we give a complete classification of schemes of abstract perspectives between two tetrahedrons such that intersecting edges corespond under this perspective to intersecting edges.
In the paper we introduce and study a classification of finite (simple, undirected, loopless) graphs with respect to a switch-equivalence (`local-complement' equivalence of \cite{pascvebl}, an analogue of the complement-equivalence of \cite{conell}). In the paper we propose a simple inductive method to compute the number of switch-types of graphs on $n$ vertices and we show that there are exactly 16 such types of graphs on 6 vertices.
In the paper we study the structure of hyperplanes of so called binomial partial Steiner triple systems (BSTS's, in short) i.e. of configurations with $\binom{n}{2}$ points and $\binom{n}{3}$ lines, each line of the size $3$. Consequently, a BSTS has $n-2$ lines through each of its points.
We introduce an operation of a kind of product which associates with a partial Steiner triple system another partial Steiner triple system, the starting one being a quotient of the result. We discuss relations of our product to some other product-like constructions and prove some preservation/non-preservation theorems. In particular, we show series of anti-Pasch Steiner triple systems which are obtained that way.
Using the technique of quasi difference sets we characterize geometry and automorphisms of configurations which can be presented as a join of some others, in particular - which can be presented as series of cyclically inscribed copies of another configuration.
We propose some new method of constructing configurations, which consists in consecutive inscribing copies of one underlying configuration. A uniform characterization of the obtained class and the one introduced in our paper untitled "Multiplied configurations, series induced by correlations", which makes use of some covering by family of closed substructures, is given.