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  2. Lehmer code - Wikipedia

    en.wikipedia.org/wiki/Lehmer_code

    In mathematics and in particular in combinatorics, the Lehmer code is a particular way to encode each possible permutation of a sequence of n numbers. It is an instance of a scheme for numbering permutations and is an example of an inversion table. The Lehmer code is named in reference to D. H. Lehmer, [1] but the code had been known since 1888 ...

  3. Simplex noise - Wikipedia

    en.wikipedia.org/wiki/Simplex_noise

    Then the resulting simplex is composed of the vertices corresponding to an ordered edge traversal from (0, 0, ..., 0) to (1, 1, ..., 1), of which there are n! possibilities, each of which corresponds to a single permutation of the coordinate. In other words, start with the zero coordinate and successively add-ones starting in the value ...

  4. Heap's algorithm - Wikipedia

    en.wikipedia.org/wiki/Heap's_algorithm

    In a 1977 review of permutation-generating algorithms, Robert Sedgewick concluded that it was at that time the most effective algorithm for generating permutations by computer. [2] The sequence of permutations of n objects generated by Heap's algorithm is the beginning of the sequence of permutations of n+1 objects.

  5. Perlin noise - Wikipedia

    en.wikipedia.org/wiki/Perlin_noise

    Two-dimensional slice through 3D Perlin noise at z = 0. Perlin noise is a type of gradient noise developed by Ken Perlin in 1983. It has many uses, including but not limited to: procedurally generating terrain, applying pseudo-random changes to a variable, and assisting in the creation of image textures.

  6. DES supplementary material - Wikipedia

    en.wikipedia.org/wiki/DES_supplementary_material

    This table specifies the input permutation on a 64-bit block. The meaning is as follows: the first bit of the output is taken from the 58th bit of the input; the second bit from the 50th bit, and so on, with the last bit of the output taken from the 7th bit of the input.

  7. Costas array - Wikipedia

    en.wikipedia.org/wiki/Costas_array

    A Costas array may be represented numerically as an n×n array of numbers, where each entry is either 1, for a point, or 0, for the absence of a point. When interpreted as binary matrices, these arrays of numbers have the property that, since each row and column has the constraint that it only has one point on it, they are therefore also permutation matrices.

  8. 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.

  9. Combinations and permutations - Wikipedia

    en.wikipedia.org/wiki/Combinations_and_permutations

    Combinations and permutations in the mathematical sense are described in several articles. Described together, in-depth: Twelvefold way; Explained separately in a more accessible way: Combination; Permutation; For meanings outside of mathematics, please see both words’ disambiguation pages: Combination (disambiguation) Permutation ...

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