Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Mariusz Żynel"'
Publikováno v:
Ars Mathematica Contemporanea. 20:151-170
The concept of the spine geometry over a polar Grassmann space belongs to a wide family of partial affine line spaces. It is known that the geometry of a spine space over a projective Grassmann space can be developed in terms of points, so called aff
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https://explore.openaire.eu/search/publication?articleId=doi_________::43448d65c9f8eaeecf0dad2a5610942d
https://doi.org/10.26493/1855-3974.2201.b65
https://doi.org/10.26493/1855-3974.2201.b65
Autor:
Krzysztof Prażmowski, Mariusz Żynel
Publikováno v:
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. 61:507-513
In the note we show that the conjugacy of points determined by a correlation of a space of pencils is definitionally equivalent to (suitably defined) orthogonality of lines and to a ‘polarity’, introduced in the space in question. This proves tha
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https://explore.openaire.eu/search/publication?articleId=doi_________::cef0895a5b51f035e27613712777a9a1
https://doi.org/10.1007/s13366-019-00480-9
https://doi.org/10.1007/s13366-019-00480-9
Two distinct projections of finite rank $m$ are adjacent if their difference is an operator of rank two or, equivalently, the intersection of their images is $(m-1)$-dimensional. We extend this adjacency relation on other conjugacy classes of finite-
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::736b2d7d51bf009db61afab00aa74698
http://arxiv.org/abs/2006.15581
http://arxiv.org/abs/2006.15581
Autor:
Mariusz Żynel, Krzysztof Prażmowski
Publikováno v:
Journal of Geometry. 110
Deleting a hyperplane from a polar space associated with a symplectic polarity we get a specific, symplectic, affine polar space. Similar geometry, called an affine semipolar space arises as a result of generalization of the notion of an alternating
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7e77d6f42b99adf9c2b15a1711da754d
https://doi.org/10.1007/s00022-019-0494-y
https://doi.org/10.1007/s00022-019-0494-y
Publikováno v:
TURKISH JOURNAL OF MATHEMATICS. 42
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6cf0be4e5c2c91b23420e715094a32ac
https://doi.org/10.3906/mat-1703-55
https://doi.org/10.3906/mat-1703-55
Autor:
Krzysztof Petelczyc, Mariusz Żynel
Publikováno v:
Ars mathematica contemporanea
In a polar space, embeddable into a projective space, we fix a subspace, that is contained in some hyperplane. The complement of that subspace resembles a slit space or a semiaffine space. We prove that under some assumptions the ambient polar space
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c8f568668d51329fc0b558dffb8c395a
http://arxiv.org/abs/1805.00229
http://arxiv.org/abs/1805.00229
Autor:
Mariusz Żynel, Krzysztof Petelczyc
Publikováno v:
Aequationes mathematicae. 90:607-623
The structure of lines in a projective or a polar Grassmann space together with binary coplanarity is a sufficient system of primitive notions for these geometries.
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::485edd42a3b9ec7d7eda69c1c5d257a7
https://doi.org/10.1007/s00010-015-0387-6
https://doi.org/10.1007/s00010-015-0387-6
Autor:
Mariusz Żynel, Jacek Konarzewski
Publikováno v:
Journal of Applied Logic. 11:169-173
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.
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https://doi.org/10.1016/j.jal.2013.01.001
https://doi.org/10.1016/j.jal.2013.01.001
Autor:
Krzysztof Petelczyc, Mariusz Żynel
Spine spaces can be considered as fragments of a projective Grassmann space. We prove that the structure of lines together with a binary coplanarity relation, as well as with the binary relation of being in one pencil of lines, is a sufficient system
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::74bc2382895a9006ad33ead3cc4cdf6d
http://arxiv.org/abs/1612.01318
http://arxiv.org/abs/1612.01318
Autor:
Mariusz Żynel
Publikováno v:
Journal of Applied Logic. 10(2):187-198
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 und
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