Geodesic
Strongly $(s-2)$-uniform extensions of partial geometries $pG_\alpha(s,t)$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 244-257

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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. 
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     title = {Strongly $(s-2)$-uniform extensions of partial geometries $pG_\alpha(s,t)$},
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M. S. Nirova. Strongly $(s-2)$-uniform extensions of partial geometries $pG_\alpha(s,t)$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 244-257. http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a23/