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Dive into the research topics where Mariusz Żynel is active.

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Featured researches published by Mariusz Żynel.


Demonstratio Mathematica | 2006

Geometry of polar Grassmann spaces

Mark Pankov; Krzysztof Prażmowski; Mariusz Żynel

The Grassmann space of fc-subspaces of a polar space is defined and its geometry is examined. In particular, its cliques, subspaces and automorphisms are characterized. An analogue of Chows theorem for the Grassmann space of fc-subspaces of a polar spaces is proved.


Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg | 2005

Transformations preserving adjacency and base subsets of spine spaces

Mark Pankov; Krzysztof Prażmowski; Mariusz Żynel

Transformations of spine spaces which preserve base subsets preserve also adjacency. They either preserve the two sorts of projective adjacency or interchange them. Lines of a spine space can be defined in terms of adjacency, except one case where projective lines have no proper extensions to projective maximal strong subspaces, and thus adjacency preserving transformations are collineations.


Journal of Applied Logic | 2012

Correlations of spaces of pencils

Mariusz Żynel

Abstract The paper introduces an axiomatic system of a conjugacy in partial linear spaces, and provides its analytical characterization in spaces of pencils. A correlation of a space of pencils is defined and it is shown to correspond to a polarity of the underlying projective space, i.e. to a reflexive sesqui-linear form, or also to an involutory collineation, i.e. to an injective semi-linear map, in the self-dual case. A geometric characterization of segment subspaces in spaces of pencils is also provided.


Journal of Applied Logic | 2010

Possible primitive notions for geometry of spine spaces

Krzysztof Prażmowski; Mariusz Żynel

Abstract New systems of notions specific to the geometry of spine spaces, are introduced. In particular parallelism turns out to be a sufficient primitive notion to express the geometry of a spine space, and we show that structures related to projective closure are definitionally equivalent to spine spaces.


Journal of Applied Logic | 2015

The complement of a point subset in a projective space and a Grassmann space

Krzysztof Petelczyc; Mariusz Żynel

Abstract In a projective space we fix some set of points, a horizon, and investigate the complement of that horizon. We prove, under some assumptions on the size of lines, that the ambient projective space, together with its horizon, both can be recovered in that complement. Then we apply this result to show something similar for Grassmann spaces.


Journal of Applied Logic | 2013

A note on orthogonality of subspaces in Euclidean geometry

Jacek Konarzewski; Mariusz Żynel

We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.


Journal of Geometry | 2004

Geometry of the structure of linear complements

Krzysztof Prażmowski; Mariusz Żynel


Advances in Geometry | 2011

Orthogonality of subspaces in metric-projective geometry

Krzysztof Prażmowski; Mariusz Żynel


Aequationes Mathematicae | 2016

Coplanarity of lines in projective and polar Grassmann spaces

Krzysztof Petelczyc; Mariusz Żynel


Aequationes Mathematicae | 2014

Complements of Grassmann substructures in projective Grassmannians

Mariusz Żynel

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Mark Pankov

Information Technology University

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