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  2. 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.

  3. 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.

  4. 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 ...

  5. 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.

  6. Inversion (discrete mathematics) - Wikipedia

    en.wikipedia.org/wiki/Inversion_(discrete...

    The identity is its minimum, and the permutation formed by reversing the identity is its maximum. If a permutation were assigned to each inversion set using the element-based definition, the resulting order of permutations would be that of a Cayley graph, where an edge corresponds to the swapping of two elements on consecutive places. This ...

  7. 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.

  8. Permuted congruential generator - Wikipedia

    en.wikipedia.org/.../Permuted_Congruential_Generator

    Finally, if a generator period longer than 2 128 is required, the generator can be extended with an array of sub-generators. One is chosen (in rotation) to be added to the main generator's output, and every time the main generator's state reaches zero, the sub-generators are cycled in a pattern which provides a period equal to 2 to the power of ...

  9. Steinhaus–Johnson–Trotter algorithm - Wikipedia

    en.wikipedia.org/wiki/Steinhaus–Johnson...

    The ! permutations of the numbers from 1 to may be placed in one-to-one correspondence with the ! numbers from 0 to ! by pairing each permutation with the sequence of numbers that count the number of positions in the permutation that are to the right of value and that contain a value less than (that is, the number of inversions for which is the ...

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