# lexicographic order

## 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.
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References in periodicals archive ?
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.
t], t [greater than or equal to] 0, let us enumerate the states of this process in the direct lexicographic order of the components r, n, w, v, m, and refer to the set of the states of the Markov chain having values (i, r) of the first two components of the Markov chain as the macrostate (i, r).
L], called the lexicographic order, on the set of partitions of n, as follows.
By convention, Apriori assumes that items within a transaction or itemset are sorted in lexicographic order.
By default we order them using the lexicographic order of the coordinates.
The comparison of linguistic information represented by 2-tuples is carried out according to an ordinary lexicographic order.
Notice that this implication does not require positive lexicographic order.
n] which inherits the lexicographic order, and we call the high term of [rho] is the highest [w.
1]] represents a one- dimensional image column obtained from the two-dimensional image patches scanned in lexicographic order and writing them into a column vector.
If the lexicographic order is introduced into these sequences, there will always be a unique minimum value or maximum value.
The lexicographic order is total, that is, any two vectors can be compared.

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