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Questions related to the field of Combinatorics called Matroid Theory. Relevant topics include matroids in Combinatorial Optimization, Lattice Theory, Algebraic Geometry, Polyhedral Theory, Rigidity, and Algorithms. For questions about Oriented Matroids, the oriented-matroids tag may be used.
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Upper bound on number of lines in a linear space given degree bounds
Let $(S,\mathcal{L})$ be a linear space and $q$ be a prime power such that
Every point in $S$ lies on at most $q+1$ lines, and
Every line in $\mathcal{L}$ contains at most $q+1$ points, and at lea …