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The lexicographic order on the resulting sequences induces thus an order on the subsets, which is also called the lexicographical order. In this context, one generally prefer to sort first the subsets by cardinality, such as in the shortlex order. Therefore, in the following, we will consider only orders on subsets of fixed cardinal.
Toggle Word order subsection. 2.1 Ending sentence with ... The following is a partial list of linguistic example sentences illustrating various linguistic phenomena.
In order of increasing strength, i.e., decreasing sets of pairs, three of the possible partial orders on the Cartesian product of two partially ordered sets are (see Fig. 4): the lexicographical order: (a, b) ≤ (c, d) if a < c or (a = c and b ≤ d); the product order: (a, b) ≤ (c, d) if a ≤ c and b ≤ d;
Heatmaps of each of the non-finite classes are shown on the right. The lexicographically minimal symmetry is used for each class, and the classes are ordered in lexicographical order. To create each heatmap, one million permutations of length 300 were sampled uniformly at random from the class.
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]
If one concatenates together, in lexicographic order, all the Lyndon words that have length dividing a given number n, the result is a de Bruijn sequence, a circular sequence of symbols such that each possible length-n sequence appears exactly once as one of its contiguous subsequences. For example, the concatenation of the binary Lyndon words ...
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 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]
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