1 citations · 1 across the 15 of their papers we have counts for
16 papers
The full automorphism groups of the five symmetric -designs
Mark Pankov, Krzysztof Petelczyc, Mariusz Żynel
It is clear that the full automorphism group of the -design of points and hyperplane complements of is . Using methods of point-line geomet…
Symmetric -designs in terms of the geometry of binary simplex codes of dimension
Mark Pankov, Krzysztof Petelczyc, Mariusz Żynel
Let and for a certain . Consider the point-line geometry of -element subsets of an -element set. Maximal singular subspaces of this geometry co…
Point-line geometries related to binary equidistant codes
Mark Pankov, Krzysztof Petelczyc, Mariusz Zynel
We investigate point-line geometries whose singular subspaces correspond to binary equidistant codes. The main result is a description of automorphisms of these geometries. In some…
Automorphisms of graphs corresponding to conjugacy classes of finite-rank self-adjoint operators
Mark Pankov, Krzysztof Petelczyc, Mariusz Zynel
We consider the graph whose vertex set is a conjugacy class consisting of finite-rank self-adjoint operators on a complex Hilbert space . The dimension of is…
Automorphisms and some geodesic properties of ortho-Grassmann graphs
Mark Pankov, Krzysztof Petelczyc, Mariusz Zynel
Let be a complex Hilbert space. Consider the ortho-Grassmann graph whose vertices are -dimensional subspaces of (projections of rank ) and two subs…
Generalized Grassmann graphs associated to conjugacy classes of finite-rank self-adjoint operators
Mark Pankov, Krzysztof Petelczyc, Mariusz Zynel
Two distinct projections of finite rank are adjacent if their difference is an operator of rank two or, equivalently, the intersection of their images is -dimensional. W…
The complement of a subspace in a classical polar space
Krzysztof Petelczyc, Mariusz Żynel
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 semiaffin…
Geometry on the lines of spine spaces
K. Petelczyc, M. Żynel
Spine spaces can be considered as fragments of a projective Grassmann space. We prove that the structure of lines together with binary coplanarity relation, as well as with binary…
Affinization of Segre products of partial linear spaces
K. Petelczyc, M. Żynel
Hyperplanes and hyperplane complements in the Segre product of partial linear spaces are investigated . The parallelism of such a complement is characterized in terms of the point-…
Hyperplanes, parallelisms, and related problems in the theory of Veronese Spaces
K. Petelczyc, K. Prażmowski, M. Prażmowska +1
We study parallelisms on Veronese spaces associated with affine spaces, determine hyperplanes in Veronese spaces associated with projective spaces, and analyse the geometry of para…
The complement of a point subset in a projective space and a Grassmann space
Mariusz Żynel, Krzysztof Petelczyc
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…
Affine polar spaces derived from polar spaces and Grassmann structures defined on them
K. Prażmowski, M. Żynel
We prove that an affine polar space in the meaning of Cohen and Shult can be recovered from one of the three adjacency relations on a Grassmann structure over it. The result direct…
Projective symplectic geometry on regular subspaces; Grassmann spaces over symplectic copolar spaces
M. Prażmowska, K. Prażmowski, M. Żynel
We construct Grassmann spaces associated with the incidence geometry of regular and tangential subspaces of a symplectic copolar space, show that the underlying metric projective s…
A note on orthogonality of subspaces in Euclidean geometry
J. Konarzewski, M. 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.
Affine polar spaces derived from symplectic spaces, their geometry and representations: alternating semiforms
K. Prażmowski, M. Żynel
Deleting a hyperplane from a polar space associated with a symplectic polarity we get a specific, symplectic, affine polar space. Similar geometry, called an \afsempol\ arises as a…
Grassmannians of lines defined in the geometry of a pseudo-polarity
K. Prażmowski, M. Żynel
The regular point-line geometry with respect to a pseudo-polarity is introduced. It is weaker than the underlying metric-projective geometry. The automorphism group of this geometr…