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  2. Birthday problem - Wikipedia

    en.wikipedia.org/wiki/Birthday_problem

    In an alternative formulation of the birthday problem, one asks the average number of people required to find a pair with the same birthday. If we consider the probability function Pr[n people have at least one shared birthday], this average is determining the mean of the distribution, as opposed to the customary formulation, which asks for the ...

  3. Lehmer code - Wikipedia

    en.wikipedia.org/wiki/Lehmer_code

    The usual way to prove that there are n! different permutations of n objects is to observe that the first object can be chosen in n different ways, the next object in n − 1 different ways (because choosing the same number as the first is forbidden), the next in n − 2 different ways (because there are now 2 forbidden values), and so forth.

  4. Permutation codes - Wikipedia

    en.wikipedia.org/wiki/Permutation_Codes

    The minimum distance of a permutation code is defined to be the minimum positive integer such that there exist ,, distinct, such that (,) =. One of the reasons why permutation codes are suitable for certain channels is that the alphabet symbols only appear once in each codeword, which for example makes the errors occurring in the context of ...

  5. 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 ...

  6. File:Permutation matrices.pdf - Wikipedia

    en.wikipedia.org/wiki/File:Permutation_matrices.pdf

    This file contains additional information, probably added from the digital camera or scanner used to create or digitize it. If the file has been modified from its original state, some details may not fully reflect the modified file.

  7. 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.

  8. Birthday attack - Wikipedia

    en.wikipedia.org/wiki/Birthday_attack

    A birthday attack is a bruteforce collision attack that exploits the mathematics behind the birthday problem in probability theory. This attack can be used to abuse communication between two or more parties. The attack depends on the higher likelihood of collisions found between random attack attempts and a fixed degree of permutations ...

  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 ...