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  2. Cyclic permutation - Wikipedia

    en.wikipedia.org/wiki/Cyclic_permutation

    A cyclic permutation consisting of a single 8-cycle. There is not widespread consensus about the precise definition of a cyclic permutation. Some authors define a permutation σ of a set X to be cyclic if "successive application would take each object of the permuted set successively through the positions of all the other objects", [1] or, equivalently, if its representation in cycle notation ...

  3. 142857 - Wikipedia

    en.wikipedia.org/wiki/142857

    If multiplying by an integer greater than 7, there is a simple process to get to a cyclic permutation of 142857. By adding the rightmost six digits (ones through hundred thousands) to the remaining digits and repeating this process until only six digits are left, it will result in a cyclic permutation of 142857: [citation needed] 142857 × 8 ...

  4. Levi-Civita symbol - Wikipedia

    en.wikipedia.org/wiki/Levi-Civita_symbol

    In two dimensions, the Levi-Civita symbol is defined by: = {+ (,) = (,) (,) = (,) = The values can be arranged into a 2 × 2 antisymmetric matrix: = (). Use of the two-dimensional symbol is common in condensed matter, and in certain specialized high-energy topics like supersymmetry [1] and twistor theory, [2] where it appears in the context of 2-spinors.

  5. Transposable integer - Wikipedia

    en.wikipedia.org/wiki/Transposable_integer

    For any integer coprime to 10, its reciprocal is a repeating decimal without any non-recurring digits. E.g. 1 ⁄ 143 = 0. 006993 006993 006993.... While the expression of a single series with vinculum on top is adequate, the intention of the above expression is to show that the six cyclic permutations of 006993 can be obtained from this repeating decimal if we select six consecutive digits ...

  6. Cyclic number - Wikipedia

    en.wikipedia.org/wiki/Cyclic_number

    A cyclic number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely known is the six-digit number 142857, whose first six integer multiples are 142857 × 1 = 142857 142857 × 2 = 285714 142857 × 3 = 428571 142857 × 4 = 571428 142857 × 5 = 714285 142857 × 6 = 857142

  7. Symmetric group - Wikipedia

    en.wikipedia.org/wiki/Symmetric_group

    Along with the special linear group SL(2, 5) and the icosahedral group A 5 × S 2, S 5 is one of the three non-solvable groups of order 120, up to isomorphism. S 5 is the Galois group of the general quintic equation, and the fact that S 5 is not a solvable group translates into the non-existence of a general formula to solve quintic polynomials by

  8. List of permutation topics - Wikipedia

    en.wikipedia.org/wiki/List_of_permutation_topics

    Enumerations of specific permutation classes; Factorial. Falling factorial; Permutation matrix. Generalized permutation matrix; Inversion (discrete mathematics) Major index; Ménage problem; Permutation graph; Permutation pattern; Permutation polynomial; Permutohedron; Rencontres numbers; Robinson–Schensted correspondence; Sum of permutations ...

  9. Circular shift - Wikipedia

    en.wikipedia.org/wiki/Circular_shift

    Cyclic codes are a kind of block code with the property that the circular shift of a codeword will always yield another codeword. This motivates the following general definition: For a string s over an alphabet Σ , let shift ( s ) denote the set of circular shifts of s , and for a set L of strings, let shift ( L ) denote the set of all ...

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