Urutan Leksikografis

Orderings of the 3-subsets of (and the corresponding binary vectors)
When the (blue) triples are in lex order the (red) vectors are in revlex order, and vice versa. The arrangements on the right side show and revcolex order.

Dalam matematika, urutan leksikografik, (biasa dikenal sebagai urutan leksikal atau urutan alfabet, adalah bentuk umum dari urutan alfabet kata yang berdasarkan pada pengurutan huruf depan.

Definisi

Diberikan dua himpunan terurut sebagian yaitu A dan B,. Leksikografik urutan di dalam Cartesian product A × B is defined as

(a,b) ≤ (a′,b′) if and only if a < a′ or (a = a′ and bb′).

The result is a partial order. If A and B are totally ordered, then the result is a total order as well.

More generally, one can define the lexicographic order on the Cartesian product of n ordered sets, on the Cartesian product of a countably infinite family of ordered sets, and on the union of such sets.