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  2. Lexicographic order - Wikipedia

    en.wikipedia.org/wiki/Lexicographic_order

    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 ...

  3. Lexicographic code - Wikipedia

    en.wikipedia.org/wiki/Lexicographic_code

    The theory of lexicographic codes is closely connected to combinatorial game theory. In particular, the codewords in a binary lexicographic code of distance d encode the winning positions in a variant of Grundy's game , played on a collection of heaps of stones, in which each move consists of replacing any one heap by at most d − 1 smaller ...

  4. Lehmer code - Wikipedia

    en.wikipedia.org/wiki/Lehmer_code

    Other properties of the Lehmer code include that the lexicographical order of the encodings of two permutations is the same as that of their sequences (σ 1, ..., σ n), that any value 0 in the code represents a right-to-left minimum in the permutation (i.e., a σ i smaller than any σ j to its right), and a value n − i at position i ...

  5. Sorting algorithm - Wikipedia

    en.wikipedia.org/wiki/Sorting_algorithm

    Merge sort. In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order.The most frequently used orders are numerical order and lexicographical order, and either ascending or descending.

  6. Lexicographic breadth-first search - Wikipedia

    en.wikipedia.org/wiki/Lexicographic_breadth...

    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.

  7. String (computer science) - Wikipedia

    en.wikipedia.org/wiki/String_(computer_science)

    If the alphabet Σ has a total order (cf. alphabetical order) one can define a total order on Σ * called lexicographical order. The lexicographical order is total if the alphabetical order is, but is not well-founded for any nontrivial alphabet, even if the alphabetical order is.

  8. Path ordering (term rewriting) - Wikipedia

    en.wikipedia.org/wiki/Path_ordering_(term_rewriting)

    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 .

  9. Gröbner basis - Wikipedia

    en.wikipedia.org/wiki/Gröbner_basis

    On the contrary, the lexicographical order is, almost always, the most difficult to compute, and using it makes impractical many computations that are relatively easy with graded reverse lexicographic order (grevlex), or, when elimination is needed, the elimination order (lexdeg) which restricts to grevlex on each block of variables.