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  2. Fisher–Yates shuffle - Wikipedia

    en.wikipedia.org/wiki/Fisher–Yates_shuffle

    The algorithm takes a list of all the elements of the sequence, and continually determines the next element in the shuffled sequence by randomly drawing an element from the list until no elements remain. [1] The algorithm produces an unbiased permutation: every permutation is equally likely.

  3. Permutation class - Wikipedia

    en.wikipedia.org/wiki/Permutation_class

    A permutation class may also be known as a pattern class, closed class, or simply class of permutations. Every permutation class can be defined by the minimal permutations which do not lie inside it, its basis. [2] A principal permutation class is a class whose basis consists of only a single permutation. Thus, for instance, the stack-sortable ...

  4. Birthday problem - Wikipedia

    en.wikipedia.org/wiki/Birthday_problem

    The birthday paradox is the counterintuitive fact that only 23 people are needed for that probability to exceed 50%. The birthday paradox is a veridical paradox: it seems wrong at first glance but is, in fact, true. While it may seem surprising that only 23 individuals are required to reach a 50% probability of a shared birthday, this result is ...

  5. 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 ...

  6. Stack-sortable permutation - Wikipedia

    en.wikipedia.org/wiki/Stack-sortable_permutation

    The stack-sortable permutations are exactly the permutations that do not contain the permutation pattern 231; they are counted by the Catalan numbers, and may be placed in bijection with many other combinatorial objects with the same counting function including Dyck paths and binary trees.

  7. Random permutation - Wikipedia

    en.wikipedia.org/wiki/Random_permutation

    A simple algorithm to generate a permutation of n items uniformly at random without retries, known as the Fisher–Yates shuffle, is to start with any permutation (for example, the identity permutation), and then go through the positions 0 through n − 2 (we use a convention where the first element has index 0, and the last element has index n − 1), and for each position i swap the element ...

  8. “Do I Have to Invite the Whole Class?” The 7 Rules of Kids ...

    www.aol.com/invite-whole-class-7-rules-180000477...

    Meier has a better idea: “With a class size of 20+ kids, it’s OK to edit the list. What isn’t OK is if there are 20 kids in the class and you invite 15 of them. In other words, you include ...

  9. Permutation pattern - Wikipedia

    en.wikipedia.org/wiki/Permutation_pattern

    A closed class, also known as a pattern class, permutation class, or simply class of permutations is a downset in the permutation pattern order. Every class can be defined by the minimal permutations which do not lie inside it, its basis. Thus the basis for the stack-sortable permutations is {231}, while the basis for the deque-sortable ...