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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2011, Volume 17, Number 4, Pages 244–257
(Mi timm768)
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Strongly $(s-2)$-uniform extensions of partial geometries $pG_\alpha(s,t)$
M. S. Nirova Kabardino-Balkar State University
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
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
Linking options:
https://www.mathnet.ru/eng/timm768 https://www.mathnet.ru/eng/timm/v17/i4/p244
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Abstract page: | 188 | Full-text PDF : | 66 | References: | 39 |
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