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In fact, with positional notation, a natural number is represented by a sequence of numerical digits, and a natural number is larger than another one if either it has more digits (ignoring leading zeroes) or the number of digits is the same and the first (most significant) digit which differs is larger.
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 ...
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.
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.
A concrete recipe for the graded reverse lexicographic order is thus to compare by the total degree first, then compare exponents of the last indeterminate x n but reversing the outcome (so the monomial with smaller exponent is larger in the ordering), followed (as always only in case of a tie) by a similar comparison of x n−1, and so forth ...
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.
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While k and m are less than N, compare S[k] (the k-th symbol of the string S) to S[m]. There are three possible outcomes: S[k] is equal to S[m]: append S[m] to the current collected symbols. Increment k and m. 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 ...