What Is Dictionary Order - Search
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    Upvotes196Top Answeredited Mar 24, 2018 at 15:47

    lexicographical order is alphabetical order. The other type is numerical ordering. Consider the following values,

    1, 10, 2

    Those values are in lexicographical order. 10 comes after 2 in numerical order, but 10 comes before 2 in "alphabetical" order.

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    Lexicographic order - Wikipedia

    In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and … See more

    Colexicographic order image

    The words in a lexicon (the set of words used in some language) have a conventional ordering, used in dictionaries and encyclopedias, that depends on the underlying ordering of the alphabet of symbols used to … See more

    The lexicographical order is used not only in dictionaries, but also commonly for numbers and dates.
    One of the drawbacks of the Roman numeral system is that it is not always immediately obvious which of … See more

    The monoid of words over an alphabet A is the free monoid over A. That is, the elements of the monoid are the finite sequences (words) of elements of A (including the empty sequence, of length 0), and the operation (multiplication) is the concatenation of … See more

    The lexicographical order defines an order on an n-ary Cartesian product of ordered sets, which is a total order when all these sets are themselves totally ordered. An element of a Cartesian product $${\displaystyle E_{1}\times \cdots \times E_{n}}$$ is … See more

    Let $${\displaystyle \mathbb {Z} ^{n}}$$ be the free Abelian group of rank $${\displaystyle n,}$$ whose elements are sequences of $${\displaystyle n}$$ integers, and operation is the addition. A group order on $${\displaystyle \mathbb {Z} ^{n}}$$ See more

    The colexicographic or colex order is a variant of the lexicographical order that is obtained by reading finite sequences from the right to the left instead of reading them from the left to the right. More precisely, whereas the lexicographical order between two … See more

    When considering polynomials, the order of the terms does not matter in general, as the addition is commutative. However, some algorithms, such as polynomial long division, require the terms to be in a specific order. Many of the main algorithms for See more

     
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