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  2. 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 ...

  3. 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 ...

  4. Twelvefold way - Wikipedia

    en.wikipedia.org/wiki/Twelvefold_way

    In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number.

  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. 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 ...

  7. Additional Mathematics - Wikipedia

    en.wikipedia.org/wiki/Additional_Mathematics

    Each question may contain from zero to three subsets of questions with marks ranging from 2 to 8 marks. The total weighting of the paper is 80 marks and constitutes 44% of the grade. Paper 2 (Duration: 2 hours 30 minutes): Questions are categorised into 3 sections: A, B and C. Section A contains 7 questions which must all be answered.

  8. Combinatorics - Wikipedia

    en.wikipedia.org/wiki/Combinatorics

    Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures.It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.

  9. Inclusion–exclusion principle - Wikipedia

    en.wikipedia.org/wiki/Inclusion–exclusion...

    In the given example, there are 12 = 2(3!) permutations with property P 1, 6 = 3! permutations with property P 2 and no permutations have properties P 3 or P 4 as there are no restrictions for these two elements. The number of permutations satisfying the restrictions is thus: 4! − (12 + 6 + 0 + 0) + (4) = 24 − 18 + 4 = 10.

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