lexicographical order in a sentence

Examples

1. The " Close by One " algorithm, for instance, generates concepts in the lexicographical order of their extents assuming that there is a linear order on the set of objects.
2. In the context of strings on a totally ordered alphabet, the "'shortlex order "'is identical to the lexicographical order, except that shorter strings precede longer strings.
3. An important property of the lexicographical order on words of a fixed length on a finite alphabet is that it is a well-order, that is, every decreasing sequence of words is finite.
4. One variant widely used in combinatorics orders subsets of a given finite set by assigning a total order to the finite set, and converting subsets into increasing sequences, to which the lexicographical order is applied.
5. Given two different sequences of the same length, and, the first one is smaller than the second one for the lexicographical order, if ( for the order of ), for the first where and differ.
6. A useful property of the degree reverse lexicographical order is that a homogeneous polynomial is a multiple of the least indeterminate if and only if its leading monomial ( its greater monomial ) is a multiple of this least indeterminate.
7. The lexicographical order on this set is a well ordering that resembles the ordering of natural numbers written in decimal notation, except with digit positions reversed, and with arbitrary natural numbers instead of just the digits 0 9:
8. It is, historically, the first to have been used for defining Gr�bner bases, and is sometimes called " pure lexicographical order " for distinguishing it from other orders that are also related to a lexicographical order.
9. It is, historically, the first to have been used for defining Gr�bner bases, and is sometimes called " pure lexicographical order " for distinguishing it from other orders that are also related to a lexicographical order.
10. Correspondence of lexicographical order and chronological order is preserved ( just like with the ISO year-week-weekday numbering ), but partial weeks make some computations of weekly statistics or payments inaccurate at end of December or beginning of January.