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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.
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 ...
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 ...
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 ...
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.
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 ...
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 ...
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 ...