PlanetMath: system of distinct representatives

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system of distinct representatives

(Definition)

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 is a set

$\displaystyle x_1 \in S_1, x_2 \in S_2, \dots x_n \in S_n$

such that

$\displaystyle x_i \neq x_j$ whenever $\displaystyle i \neq j$

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

"system of distinct representatives" is owned by vampyr.

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Other names:

SDR

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Cross-references: finite sets, collection, finite
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This is version 1 of system of distinct representatives, born on 2002-04-16.
Object id is 2836, canonical name is SystemOfDistinctRepresentatives.
Accessed 5706 times total.

Classification:

05D15 (Combinatorics :: Extremal combinatorics :: Transversal theory)

Pending Errata and Addenda

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