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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 build the words. The lexicographical order is one way of formalizing word order given the order of the underlying symbols.
Similarly, (4,2,4) is lexicographically larger than (2,4,4). The following algorithm can be used to compute whether x is leximin-larger than y: Let x' be a vector containing the same elements of x but in ascending order; Let y' be a vector containing the same elements of y but in ascending order; Return "true" iff x' is lexicographically-larger ...
The word lexicon derives from Greek word λεξικόν (lexikon), neuter of λεξικός (lexikos) meaning 'of or for words'. [ 1 ] Linguistic theories generally regard human languages as consisting of two parts: a lexicon, essentially a catalogue of a language's words (its wordstock); and a grammar , a system of rules which allow for the ...
Lexicography is the study of lexicons and the art of compiling dictionaries. [1] It is divided into two separate academic disciplines: . Practical lexicography is the art or craft of compiling, writing and editing dictionaries.
Lexicology is the branch of linguistics that analyzes the lexicon of a specific language.A word is the smallest meaningful unit of a language that can stand on its own, and is made up of small components called morphemes and even smaller elements known as phonemes, or distinguishing sounds.
In mathematics, and particularly in the theory of formal languages, shortlex is a total ordering for finite sequences of objects that can themselves be totally ordered. In the shortlex ordering, sequences are primarily sorted by cardinality (length) with the shortest sequences first, and sequences of the same length are sorted into lexicographical order. [1]
Case 1: < (, ′), i.e. has fewer prefix characters in common with M than M has in common with M'. This means the (k+1)-th character of M' is the same as that of M, and since P is lexicographically larger than M, it must be lexicographically larger than M', too.
Even though the first option contains fewer total goods than the second option, it is preferred because it has more Y. Note that the number of X's is the same, and so the agent is comparing Y's. Even though the third option has the same total goods as the first option, the first option is still preferred because it has more X.