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Combinatorics on words is a fairly new field of mathematics, branching from combinatorics, which focuses on the study of words and formal languages. The subject looks at letters or symbols, and the sequences they form. Combinatorics on words affects various areas of mathematical study, including algebra and computer science. There have been a ...
Arithmomania (from Greek arithmós, "number", and maníā, "compulsion") is a mental disorder that may be seen as an expression of obsessive–compulsive disorder (OCD). [1] Individuals experiencing this disorder have a strong need to count their actions or objects in their surroundings.
Eve could use frequency analysis to help solve the message along the following lines: counts of the letters in the cryptogram show that I is the most common single letter, [2] XL most common bigram, and XLI is the most common trigram. e is the most common letter in the English language, th is the most common bigram, and the is the
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 only diagnosis existing in DSM-5 is obsessive–compulsive disorder. [2] According to DSM-5 compulsions can be mental, but they are always repetitive actions like "praying, counting, repeating words silently". [26] DSM-5 does not have any information that searching an answer for some question can be associated with OCD. [27]
The following Python code calculates a de Bruijn sequence, given k and n, based on an algorithm from Frank Ruskey's Combinatorial Generation. [ 10 ] from typing import Iterable , Any def de_bruijn ( k : Iterable [ str ] | int , n : int ) -> str : """de Bruijn sequence for alphabet k and subsequences of length n.
This count, either as a ratio of the total or normalized by dividing by the expected count for a random source model, is known as the index of coincidence, or IC or IOC [2] or IoC [3] for short. Because letters in a natural language are not distributed evenly , the IC is higher for such texts than it would be for uniformly random text strings.
Lyndon words are named after mathematician Roger Lyndon, who investigated them in 1954, calling them standard lexicographic sequences. [1] Anatoly Shirshov introduced Lyndon words in 1953 calling them regular words. [2] Lyndon words are a special case of Hall words; almost all properties of Lyndon words are shared by Hall words.