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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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Hall theorem with non-saturating matching

Hall's marriage theorem states that given a bipartite graph $G=(X+Y,E)$, if there is no $X$-saturating matching, there there exists $W\subseteq X$ such that $|W|>|N_G(W)|$. Is the following generaliz …
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