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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…