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distinct representative
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distinct representative

mathematics
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In mathematics, a "system of distinct representatives" (SDR) refers to a selection of elements from a collection of sets, where each selected element is unique and comes from a different set. Specifically, if you have sets (S_1, S_2, \dots, S_n), an SDR is a sequence of elements (x_1, x_2, \dots, x_n) such that each (x_i) is in (S_i), and all the (x_i) are different from each other.1

A key theorem by M. Hall, Jr. states that such a system exists if and only if any (k) of the (n) subsets collectively contain at least (k) distinct elements. This concept is important in combinatorics, dealing with problems of choice and arrangement.1

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  1. combinatorics - Systems of distinct representatives
  2. distinct

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