Partial Geometry

Definition

A partial geometry with parameters $(s,t,\alpha )$ is a partial linear space satisfying the following conditions:

• each line is incident with $s+1$ points ($s\ge 1$),
• each point is incident with $t+1$ lines $(t\ge 1)$,
• any point $p$ outside a line $L$ is collinear with a constant number $\alpha$ of points of $L$.

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ref: A classification of finite partial linear spaces with a primitive rank 3 automorphism group of almost simple type