Lesson plan
Partial geometry
An incidence structure C=(P,L,I) consists of a set of points, a set of lines, and an incidence relation, or set of flags, I \subseteq P \times L ; a point p is said to be incident with a line l if . It is a (finite) partial geometry if there are integers s,t,\alpha\geq 1 such that: * For any pair of distinct points p and , there is at most one line incident with both of them. * Each line is incident with s+1 points. * Each point is incident with t+1 lines. * If a point p and a line l are not incident, there are exactly \alpha pairs , such that p is incident with m and q is incident with . A partial geometry with these parameters is denoted by .
Article summary
An incidence structure C=(P,L,I) consists of a set of points, a set of lines, and an incidence relation, or set of flags, I \subseteq P \times L ; a point p is said to be incident with a line l if . It is a (finite) partial geometry if there are integers s,t,\alpha\geq 1 such that: * For any pair of distinct points p and , there is at most one line incident with both of them. * Each line is incident with s+1 points. * Each point is incident with t+1 lines. * If a point p and a line l are not incident, there are exactly \alpha pairs , such that p is incident with m and q is incident with . A partial geometry with these parameters is denoted by .
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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