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  2. 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.

  3. 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 ...

  4. 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 ...

  5. Superpermutation - Wikipedia

    en.wikipedia.org/wiki/Superpermutation

    For instance, in the case of n = 2, the superpermutation 1221 contains all possible permutations (12 and 21), but the shorter string 121 also contains both permutations. It has been shown that for 1 ≤ n ≤ 5, the smallest superpermutation on n symbols has length 1! + 2! + … + n! (sequence A180632 in the OEIS). The first four smallest ...

  6. Permutation group - Wikipedia

    en.wikipedia.org/wiki/Permutation_group

    a = (1 2)(3)(4) = (1 2) This permutation interchanges 1 and 2, and fixes 3 and 4. b = (1)(2)(3 4) = (3 4) Like the previous one, but exchanging 3 and 4, and fixing the others. ab = (1 2)(3 4) This permutation, which is the composition of the previous two, exchanges simultaneously 1 with 2, and 3 with 4. G 1 forms a group, since aa = bb = e, ba ...

  7. 100 prisoners problem - Wikipedia

    en.wikipedia.org/wiki/100_prisoners_problem

    Graph representations of the permutations (1 7 5)(2 4 8)(3 6) and (1 3 7 4 5 8 2)(6) The prison director's assignment of prisoner numbers to drawers can mathematically be described as a permutation of the numbers 1 to 100.

  8. Eulerian number - Wikipedia

    en.wikipedia.org/wiki/Eulerian_number

    In combinatorics, the Eulerian number (,) is the number of permutations of the numbers 1 to in which exactly elements are greater than the previous element (permutations with "ascents"). Leonhard Euler investigated them and associated polynomials in his 1755 book Institutiones calculi differentialis .

  9. Permutohedron - Wikipedia

    en.wikipedia.org/wiki/Permutohedron

    (In the example image the vertices (3, 2, 1, 4) and (2, 3, 1, 4) are connected by a blue edge and differ by swapping 2 and 3 on the first two places. The values 2 and 3 differ by 1. All blue edges correspond to swaps of coordinates on the first two places.) The number of facets is 2 n − 2, because they correspond to non-empty proper subsets S ...