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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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Group not leaving subset invariant
For the property $P$ discussed, the usual argument that $P(G_1) \wedge P(G_2) \Rightarrow P(\langle G_1, G_2\rangle)$, where $G_1$ and $G_2$ are groups and $\langle G_1, G_2\rangle$ is the group gener …