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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 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 .
In mathematics, lexicographical order is a means of ordering sequences in a manner analogous to that used to produce alphabetical order. [ 16 ] Some computer applications use a version of alphabetical order that can be achieved using a very simple algorithm , based purely on the ASCII or Unicode codes for characters.
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]
In mathematics, and particularly in the theory of formal languages, shortlex is a total ordering for finite sequences of objects that can themselves be totally ordered. In the shortlex ordering, sequences are primarily sorted by cardinality (length) with the shortest sequences first, and sequences of the same length are sorted into lexicographical order. [1]
Graded reverse lexicographic order (grevlex, or degrevlex for degree reverse lexicographic order) compares the total degree first, then uses a lexicographic order as tie-breaker, but it reverses the outcome of the lexicographic comparison so that lexicographically larger monomials of the same degree are considered to be degrevlex smaller.
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.
Lexicographic error; Lexicographic information cost; Lexicographic order; Lexicographic preferences; Lexicographically minimal string rotation; Name; Lexigraf; LexSite; Linguistic Data Consortium; List of Japanese dictionaries