nonlexicographic

Nonlexicographic is an adjective used in mathematics, computer science, and information theory to describe something that is not ordered according to a lexicographic criterion. Lexicographic order compares sequences by their first differing element and relies on the intrinsic order of the elements. Nonlexicographic concepts therefore refer to orderings, classifications, or enumerations that do not follow this dictionary-like rule.

In practice, nonlexicographic orders appear in order theory and combinatorics. Common examples of nonlexicographic ordering include colexicographic order, reverse or mixed lexicographic orders, and various partial orders. In permutation generation and coding, nonlexicographic sequences may be chosen to optimize properties other than the lexicographic progression, such as locality or minimal changes between consecutive items (for example, Gray code sequences).

In algorithm design and data organization, nonlexicographic sorting or ranking sorts elements according to attributes other than their lexical form. This can include numerical values, categorical attributes, or custom comparators defined by application requirements. The term is mainly used to contrast with lexicographic methods and is not tied to a single standard definition beyond the general idea of not following dictionary-like ordering.