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Galois geometry, finite projective and affine spaces, polar spaces, partial geometries, generalized polygons, near polygons, and other finite incidence geometries.
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Status of the basis exchange condition for symplectic matroids
Let $J_n := \{1,2,3,\ldots,n,1^*,2^*,\ldots,n^*\}$ with the involution $x\mapsto x^*$ exchanging $i$ and $i^*$ for $1\leq i\leq n$. The following is supposed to be standard, but to avoid any doubt as …