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The lexicographical order of two totally ordered sets is thus a linear extension of their product order. One can define similarly the lexicographic order on the Cartesian product of an infinite family of ordered sets, if the family is indexed by the natural numbers, or more generally by a well-ordered set. This generalized lexicographical order ...
The algorithm is called lexicographic breadth-first search because the order it produces is an ordering that could also have been produced by a breadth-first search, and because if the ordering is used to index the rows and columns of an adjacency matrix of a graph then the algorithm sorts the rows and columns into lexicographical order.
For example, the items are books, the sort key is the title, subject or author, and the order is alphabetical. A new sort key can be created from two or more sort keys by lexicographical order. The first is then called the primary sort key, the second the secondary sort key, etc.
Lexicography is the practice of creating books, computer programs, or databases that reflect lexicographical work and are intended for public use. These include dictionaries and thesauri which are widely accessible resources that present various aspects of lexicology, such as spelling, pronunciation, and meaning.
An alternative construction involves concatenating together, in lexicographic order, all the Lyndon words whose length divides n. [6] An inverse Burrows–Wheeler transform can be used to generate the required Lyndon words in lexicographic order. [7] de Bruijn sequences can also be constructed using shift registers [8] or via finite fields. [9]
The lexicographic combination of two total orders is a linear extension of their product order, and thus the product order is a subrelation of the lexicographic order. [3] The Cartesian product with the product order is the categorical product in the category of partially ordered sets with monotone functions. [7]
Some, but not all people have lexicographic preferences. Lexicographic preferences extend only to a certain quantity of the good. The nonstandard (infinitesimal) equilibrium prices for exchange can be determined for lexicographic order using standard equilibrium methods, except using nonstandard reals as the range of both utilities and prices.
the lexicographic path ordering (lpo) [5] a combination of mpo and lpo, called recursive path ordering by Dershowitz, Jouannaud (1990) [ 6 ] [ 7 ] [ 8 ] Dershowitz, Okada (1988) list more variants, and relate them to Ackermann 's system of ordinal notations .