Search results
Results from the WOW.Com Content Network
If k > 1 the remaining elements of the k-combination form the k − 1-combination corresponding to the number () in the combinatorial number system of degree k − 1, and can therefore be found by continuing in the same way for and k − 1 instead of N and k.
Square-free words do not have adjacent repeated factors. [1] To clarify, "dining" is not square-free since "in" is repeated consecutively, while "servers" is square-free, its two "er" factors not being adjacent. Thue proves his conjecture on the existence of infinite square-free words by using substitutions. A substitution is a way to take a ...
Another way to generalise the notion of a word-representable graph, again suggested by Remmel, is to introduce the "degree of tolerance" k for occurrences of a pattern p defining edges/non-edges. That is, we can say that if there are up to k occurrence of p formed by letters a and b , then there is an edge between a and b .
Initially, k = 0. 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 ...
More generally, if a pattern of length k appears a different number of times in the two words, they can be distinguished from each other using O(k log n) states. [1] If two binary words differ from each other within their first or last k positions, they can be distinguished from each other using k + O(1) states.
The English language has a number of words that denote specific or approximate quantities that are themselves not numbers. [1] Along with numerals, and special-purpose words like some, any, much, more, every, and all, they are quantifiers. Quantifiers are a kind of determiner and occur in many constructions with other determiners, like articles ...
The California Job Case was a compartmentalized box for printing in the 19th century, sizes corresponding to the commonality of letters. The frequency of letters in text has been studied for use in cryptanalysis, and frequency analysis in particular, dating back to the Arab mathematician al-Kindi (c. AD 801–873 ), who formally developed the method (the ciphers breakable by this technique go ...
The complete graph on n vertices is denoted by K n.Some sources claim that the letter K in this notation stands for the German word komplett, [4] but the German name for a complete graph, vollständiger Graph, does not contain the letter K, and other sources state that the notation honors the contributions of Kazimierz Kuratowski to graph theory.