For equal-size subsets and of an ordered ground set, precedes in lexicographic order when the smallest element of their symmetric difference belongs to .
For finite sequences over a total order, lexicographic order compares the first differing sequence terms; the smaller term determines the smaller sequence. If one sequence is a proper prefix of the other, the shorter precedes its extension. For fixed-length tuples, this is the first-difference rule used by radix sort key encoding.
The lexicographic rank of an object is its position among the admissible objects in lexicographic order. The rank convention must specify whether the first object has rank zero or one.
