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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2011, Volume 17, Number 4, Pages 244–257 (Mi timm768)  

Strongly $(s-2)$-uniform extensions of partial geometries $pG_\alpha(s,t)$

M. S. Nirova

Kabardino-Balkar State University
References:
Abstract: A geometry of rank $2$ is an incidence system $(P,\mathcal B)$, where $P$ is a set of points and $\mathcal B$ is a family of subsets from $P$, which are called blocks. Two points from $P$ are called collinear if they lie in the same block from $\mathcal B$. A pair $(a,B)$ from $(P,\mathcal B)$ is called a flag if the point $a$ belongs to the block $B$ and an antiflag otherwise. A geometry is called $\varphi$-uniform if, for any antiflag $(a,B)$, the number of points in the block $B$ that are collinear to the point $a$ is either $0$ or $\varphi$; it is called strongly $\varphi$-uniform if this number is always $\varphi$. In this paper, we study strongly $(s-2)$-uniform extensions of partial geometries $pG_\alpha(s,t)$.
Keywords: partial geometry, uniform extension.
Received: 10.04.2011
Bibliographic databases:
Document Type: Article
UDC: 519.17
Language: Russian
Citation: M. S. Nirova, “Strongly $(s-2)$-uniform extensions of partial geometries $pG_\alpha(s,t)$”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 4, 2011, 244–257
Citation in format AMSBIB
\Bibitem{Nir11}
\by M.~S.~Nirova
\paper Strongly $(s-2)$-uniform extensions of partial geometries $pG_\alpha(s,t)$
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2011
\vol 17
\issue 4
\pages 244--257
\mathnet{http://mi.mathnet.ru/timm768}
\elib{https://elibrary.ru/item.asp?id=17870441}
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