marriage theorem


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marriage theorem

[′mar·ij ‚thir·əm]
(mathematics)
The proposition that a family of n subsets of a set S with n elements is a system of distinct representatives for S if any k of the subsets, k = 1, 2, …, n, together contain at least k distinct elements. Also known as Hall's theorem.
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Notice that by Hall's marriage theorem, the condition on the [J.
Hall marriage theorem applied to our setup says that there exists an arrangement of marriages M : C([[sigma].