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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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Prescribing the dimension of intersections of sub-vector spaces
I asked this question on Mathematics Stackexchange, but got no answer.
Let $K$ be a field and $n$ a positive integer. To a finite dimensional $K$-vector space $V$, equipped with a family $V_1,\dots,V …