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In the infinite Fibonacci word, the ratio (number of letters)/(number of zeroes) is φ, as is the ratio of zeroes to ones. [4] The infinite Fibonacci word is a balanced sequence: Take two factors of the same length anywhere in the Fibonacci word. The difference between their Hamming weights (the number of occurrences of "1") never exceeds 1. [5]
Each of the n i occurrences of the i-th letter matches each of the remaining n i − 1 occurrences of the same letter. There are a total of N(N − 1) letter pairs in the entire text, and 1/c is the probability of a match for each pair, assuming a uniform random distribution of the characters (the "null model"; see below). Thus, this formula ...
We can also consider the fact that the average number of occurrences of in a random string of length is | |. This number is independent of the autocorrelation polynomial. An occurrence of may overlap another occurrence in different ways. More precisely, each 1 in its autocorrelation vector correspond to a way for occurrence to overlap.
In computer science, an FM-index is a compressed full-text substring index based on the Burrows–Wheeler transform, with some similarities to the suffix array.It was created by Paolo Ferragina and Giovanni Manzini, [1] who describe it as an opportunistic data structure as it allows compression of the input text while still permitting fast substring queries.
In computer programming, a magic number is any of the following: A unique value with unexplained meaning or multiple occurrences which could (preferably) be replaced with a named constant A constant numerical or text value used to identify a file format or protocol (for files, see List of file signatures )
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Jamal Murray tops the list of guards to avoid at their current cost in 2024-25 fantasy basketball leagues amid concerns about his health ahead of the season.
A modification of Lagged-Fibonacci generators. A SWB generator is the basis for the RANLUX generator, [19] widely used e.g. for particle physics simulations. Maximally periodic reciprocals: 1992 R. A. J. Matthews [20] A method with roots in number theory, although never used in practical applications. KISS: 1993 G. Marsaglia [21]