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  2. Permutation representation - Wikipedia

    en.wikipedia.org/wiki/Permutation_representation

    Now the character of this representation is defined as the trace of this permutation matrix. An element on the diagonal of a permutation matrix is 1 if the point in is fixed, and 0 otherwise. So we can conclude that the trace of the permutation matrix is exactly equal to the number of fixed points of .

  3. Permutation - Wikipedia

    en.wikipedia.org/wiki/Permutation

    Permutations without repetition on the left, with repetition to their right. If M is a finite multiset, then a multiset permutation is an ordered arrangement of elements of M in which each element appears a number of times equal exactly to its multiplicity in M. An anagram of a word having some repeated letters is an example of a multiset ...

  4. 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.

  5. 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 ...

  6. Derangement - Wikipedia

    en.wikipedia.org/wiki/Derangement

    (n factorial) is the number of n-permutations; !n (n subfactorial) is the number of derangements – n-permutations where all of the n elements change their initial places. In combinatorial mathematics, a derangement is a permutation of the elements of a set in which no element appears in its original

  7. Permutation group - Wikipedia

    en.wikipedia.org/wiki/Permutation_group

    A permutation group is a subgroup of a symmetric group; that is, its elements are permutations of a given set. It is thus a subset of a symmetric group that is closed under composition of permutations, contains the identity permutation, and contains the inverse permutation of each of its elements. [2]

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