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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 words. A word u is a prefix (or 'truncation') of another word v if there exists a word w ...
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 ...
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.
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 ...
S[k] is less than S[m]: if we append S[m] to the current collected symbols, we'll get a Lyndon word. But we can't add it to the result list yet because it may be just a part of a larger Lyndon word. Thus, just increment m and set k to 0 so the next symbol would be compared to the first one in the string.
The word teetertotter (used in North American English) is longer at 12 letters, although it is usually spelled with a hyphen. The longest using only the middle row is shakalshas (10 letters). Nine-letter words include flagfalls; eight-letter words include galahads and alfalfas. Since the bottom row contains no vowels, no standard words can be ...
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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.