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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 ...
In their experiment, Luria and Delbrück inoculated a small number of bacteria (Escherichia coli) into separate culture tubes. After a period of growth, they plated equal volumes of these separate cultures onto agar containing the T1 phage (virus). If resistance to the virus in bacteria were caused by an induced activation in bacteria i.e. if ...
Permutation tests exist for any test statistic, regardless of whether or not its distribution is known. Thus one is always free to choose the statistic which best discriminates between hypothesis and alternative and which minimizes losses.
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 ...
Some authors restrict partial permutations so that either the domain [4] or the range [3] of the bijection is forced to consist of the first k items in the set of n items being permuted, for some k. In the former case, a partial permutation of length k from an n-set is just a sequence of k terms from the n-set without repetition.
For combinatorial tasks, permutations are usually used that are specifically designed for genomes that are themselves permutations of a set. The underlying set is usually a subset of or . If 1- or n-point or uniform crossover for integer genomes is used for such genomes, a child genome may contain some values twice and others may be missing.
A requirement that be injective means that no label can be used a second time; the result is a sequence of labels without repetition. In the absence of such a requirement, the terminology "sequences with repetition" is used, meaning that labels may be used more than once (although sequences that happen to be without repetition are also allowed).
An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated.