Zobrazeno 1 - 10
of 85
pro vyhledávání: '"Petelczyc, Krzysztof"'
Let $n=2^k-1$ and $m=2^{k-2}$ for a certain $k\ge 3$. Consider the point-line geometry of $2m$-element subsets of an $n$-element set. Maximal singular subspaces of this geometry correspond to binary simplex codes of dimension $k$. For $k\ge 4$ the as
Externí odkaz:
http://arxiv.org/abs/2406.19710
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 important cases, automorphisms induced by non-monomial linear automor
Externí odkaz:
http://arxiv.org/abs/2305.08531
Publikováno v:
In Journal of Combinatorial Theory, Series A February 2025 210
Autor:
Petelczyc, Krzysztof1 (AUTHOR), Bolek, Jan1 (AUTHOR), Kakarenko, Karol1 (AUTHOR) karol.kakarenko@pw.edu.pl, Krix-Jachym, Karolina2 (AUTHOR), Kołodziejczyk, Andrzej1 (AUTHOR), Rękas, Marek2 (AUTHOR)
Publikováno v:
PLoS ONE. 7/19/2024, Vol. 19 Issue 7, p1-22. 22p.
We consider the graph whose vertex set is a conjugacy class ${\mathcal C}$ consisting of finite-rank self-adjoint operators on a complex Hilbert space $H$. The dimension of $H$ is assumed to be not less than $3$. In the case when operators from ${\ma
Externí odkaz:
http://arxiv.org/abs/2111.02837
Let $H$ be a complex Hilbert space. Consider the ortho-Grassmann graph $\Gamma^{\perp}_{k}(H)$ whose vertices are $k$-dimensional subspaces of $H$ (projections of rank $k$) and two subspaces are connected by an edge in this graph if they are compatib
Externí odkaz:
http://arxiv.org/abs/2103.05702
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-
Externí odkaz:
http://arxiv.org/abs/2006.15581
Publikováno v:
In Linear Algebra and Its Applications 1 October 2023 674:192-207
Autor:
Petelczyc, Krzysztof, Żynel, Mariusz
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
Externí odkaz:
http://arxiv.org/abs/1805.00229
Publikováno v:
In Linear Algebra and Its Applications 15 October 2021 627:1-23