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Lyndon word information


In mathematics, in the areas of combinatorics and computer science, a Lyndon word is a nonempty string that is strictly smaller in lexicographic order than all of its rotations. 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.

  1. ^ Lyndon (1954).
  2. ^ Shirshov (1953).

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Lyndon word

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computer science, a Lyndon word is a nonempty string that is strictly smaller in lexicographic order than all of its rotations. Lyndon words are named after...

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Combinatorics on words

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A Lyndon word is a word over a given alphabet that is written in its simplest and most ordered form out of its respective conjugacy class. Lyndon words...

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Lyndon LaRouche

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Lyndon Hermyle LaRouche Jr. (September 8, 1922 – February 12, 2019) was an American political activist who founded the LaRouche movement and its main organization...

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Roger Lyndon

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known for Lyndon words, the Curtis–Hedlund–Lyndon theorem, Craig–Lyndon interpolation and the Lyndon–Hochschild–Serre spectral sequence. Lyndon was born...

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Monoid factorisation

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every word in the free monoid can be written as a concatenation of elements drawn from the subsets. The Chen–Fox–Lyndon theorem states that the Lyndon words...

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Lexicographic order

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Lexicographically minimal string rotation Leximin order Long line (topology) Lyndon word Star product, a different way of combining partial orders Shortlex order...

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De Bruijn sequence

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contain a Lyndon word as a unique minimum element, so the inverse Burrows—Wheeler transform can be considered to generate a set of Lyndon words. It can...

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Circular shift

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expression of length O(n3) describing shift(L). Barrel shifter Circulant Lyndon word Necklace — an object like a tuple but for which circular shifts are considered...

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The Luck of Barry Lyndon

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The Luck of Barry Lyndon is a picaresque novel by English author William Makepeace Thackeray, first published as a serial in Fraser's Magazine in 1844...

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Sturmian word

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the Sturm comparison theorem.: 114  Cutting sequence Word (group theory) Morphic word Lyndon word Hordijk, A.; Laan, D. A. (2001). "Bounds for Deterministic...

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Hall word

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better-known case of Lyndon words; in fact, the Lyndon words are a special case, and almost all properties possessed by Lyndon words carry over to Hall...

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Lexicographically minimal string rotation

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fast generation of certain chemical structures without repetitions. Lyndon word Knuth–Morris–Pratt algorithm Kellogg S. Booth; Colbourn, Charles J. (1980)...

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Morphic word

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D0L word with an initial segment u of length |u| ≥ |w|, then zν is a purely morphic word, where z is a letter not in A. Cutting sequence Lyndon word Hall...

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Views of Lyndon LaRouche and the LaRouche movement

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Lyndon LaRouche (1922–2019) and the LaRouche movement have expressed controversial views on a wide variety of topics. The LaRouche movement is made up...

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LaRouche movement

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LaRouche movement is a political and cultural network promoting the late Lyndon LaRouche and his ideas. It has included many organizations and companies...

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Word problem for groups

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H. (1973). "The word problem for absolute presentations". J. London Math. Soc. s2-6 (2): 275–280. doi:10.1112/jlms/s2-6.2.275. Lyndon, Roger C.; Schupp...

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Typewriter

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the Smith Corona Electra 210 to write his biographies of Robert Moses and Lyndon Johnson. Erik Satie's 1917 score for the ballet Parade includes a "Mach...

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Free Lie algebra

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bijection γ from the Lyndon words in an ordered alphabet to a basis of the free Lie algebra on this alphabet defined as follows: If a word w has length 1 then...

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Historical rankings of presidents of the United States

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showed that historians had ranked Franklin D. Roosevelt, Theodore Roosevelt, Lyndon B. Johnson, Woodrow Wilson, Harry S. Truman, John F. Kennedy, Dwight D....

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Great Society

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was a set of domestic programs in the United States launched by President Lyndon B. Johnson in 1964 and 1965. The term was first referenced during a 1964...

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