# system of distinct representatives

Let $S=\left\{S_{1},S_{2},\dots S_{n}\right\}$ be a finite collection of finite sets. A system of distinct representatives, or SDR, of $S$ is a set

 $x_{1}\in S_{1},x_{2}\in S_{2},\dots x_{n}\in S_{n}$

such that

 $x_{i}\neq x_{j}\text{ whenever }i\neq j$

(i.e., each choice must be unique).

Title system of distinct representatives SystemOfDistinctRepresentatives 2013-03-22 12:35:11 2013-03-22 12:35:11 vampyr (22) vampyr (22) 4 vampyr (22) Definition msc 05D15 SDR