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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 ...
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.
In general topology, the lexicographic ordering on the unit square (sometimes the dictionary order on the unit square [1]) is a topology on the unit square S, i.e. on the set of points (x,y) in the plane such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. [2]
Lexicographic max-min optimization is a variant of lexicographic optimization in which all objectives are equally important, and the goal is to maximize the smallest objective, then the second-smallest objective, and so on. In game theory, the nucleolus is defined as a lexicographically-minimal solution set. [6]
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.
If the edge relations of the two graphs are order relations, then the edge relation of their lexicographic product is the corresponding lexicographic order. The lexicographic product was first studied by Felix Hausdorff . As Feigenbaum & Schäffer (1986) showed, the problem of recognizing whether a graph is a lexicographic product is equivalent ...
Toggle Word order subsection. 2.1 Ending sentence with ... The following is a partial list of linguistic example sentences illustrating various linguistic phenomena.
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]