16.3: Systems of Distinct Representatives - Mathematics LibreTexts
https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Combinatorics_(Morris)/04%3A_Design_Theory/16%3A_Latin_Squares/16.03%3A_Systems_of_Distinct_Representatives
WEBThe collection of sets \ (T_1, . . . , T_n\) has a system of distinct representatives if and only if for every \ (1 ≤ k ≤ n\), the union of any \ (k\) of the sets has cardinality at least \ (k\). This theorem is often referred to as “Hall’s Marriage Theorem,” as one of the problems it solves can be stated as follows.
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