Topic summary
Lexicographic ordering
Extracted from the Wikipedia article Lexicographic order.
Colexicographic order
The main property of the colexicographical order for increasing sequences of a given length is that every initial segment is finite. In other words, the colexicographical order for increasing sequences of a given length induces an order isomorphism with the natural numbers, and allows enumerating these sequences. This is frequently used in combinatorics, for example in the proof of the Kruskal–Katona theorem. In contrast, the ellipses in the above lexicographic ordering each elide an infinity of sequences meaning that, for example, the initial segment ending with 23 is infinite.