# lexicographic order

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## lexicographic order

[¦lek·sə·kō¦graf·ik ′ȯr·dər]
(mathematics)
Given sets A and B with a common ordering <, one="" defines="" an="" ordering="" between="" all="" sequences="" (finite="" or="" infinite)="" of="" elements="" of="">A and of elements of B by (a1, a2,…) <>b1, b2,…) if either ai = bi for every i, or an <>bn , where n is the first place in which they differ; this is the way words are ordered in a dictionary.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Generating Permutations in Lexicographic Order. Ranjan Chaudhuri, Eastern Michigan University
(2) A package clustering algorithm is used to replace traditional lexicographic order methods to reduce the block matching times, where each package is used to represent a cluster.
In particular, the method is based on the minimization of a properly defined global cost function (GCF) inspired by the lexicographic order rules and named quantized lexicographic weighted sum (QLWS).
Sort them from small to large by lexicographic order. The Cantor expansion and inverse Cantor expansion indicate that there is a one-to-one correspondence between the full permutation set of C and {1, 2, ..., n!}.
We adopt matrix-vector notation such that each [y.sub.k] and x are arranged as N x 1 and PN x 1 vectors in lexicographic order, where the integer P > 1 is the factor of increase in resolution, and [square root of P] is the magnification factor.
Lexicographic order is a commonly used elimination order.
First, the gSpan constructs a new lexicographic order among graphs and maps each graph to a unique minimum depth-first search (DFS) code as its canonical label.
There are several monomial orders but we need only the lexicographic order [[??].sub.lex] in the elimination theory.
The security mechanism based on encryption/decryption algorithm needed to generate a key according to the random number (Prasad et al, 2014; Bharatesh and Rohith, 2014; Cui, 2013), and all the keys were arranged in lexicographic order.
The grid locations of the unknown u automatically follow a lexicographic order resulting from the tensor product formulation, which greatly simplifies the coding of the linear system (3.5).
For all n, define the partial order [[less than or equal to].sub.L], called the lexicographic order, on the set of partitions of n, as follows.
The order relation is the lexicographic order: (a, b) < (c, d) iff a < c or (a = c and b < d).

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