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From Steiner systems to geometric lattices to matroids

Let $B$ be the subsets of $\{1,2,...,22\}$ of size $4$ which are not contained in any block of $S(3,6,22)$. $B$ satisfies the basis exchange property. Proof: Let $X,Y\in B$, $a\in X$. $X \setminus …
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