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On the expected number of commutations in reduced words
On the expected number of commutations in reduced words

Math 230 – 2003-04 – Assignment 2 Due
Math 230 – 2003-04 – Assignment 2 Due

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q-gram Based Database Searching Using a Suffix Array (QUASAR)
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... needed to store the original data which clearly may create serious problems when applied to large data collections (see also Heu97, MH95]). Myers Mye94] suggested a sublinear (in the database size) search algorithm that is centered around an index built on small substrings of the database sequence ...
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... of the model space by using a method described by Wiggins [1969, 1972] in which the model space was sampled according to the prior distribution ρ(m). This approach is superior to a uniform sampling by crude Monte Carlo. However, the peaks of the prior distribution are typically much less pronounced ...
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... our approach, they compute an optimal solution, while we compute an approximate solution; but we provide worst-case analysis that with high probability our algorithm is guaranteed to work, while they do not. Also, the sampling complexity of their algorithm depends on the higher dimension n, while th ...
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... occurring in a total of n trials is P(0) = (1 − )n . Conversely, the probability of more than zero (i.e. at least one) such events occurring must be the complement of this (‘complement of’ means ‘one minus’), 1 − (1 − )n . Finally, remember that the binomial probability distribution is relevant fo ...
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BMT 2014 Symmetry Groups of Regular Polyhedra 22 March 2014
BMT 2014 Symmetry Groups of Regular Polyhedra 22 March 2014

... Since permutations can be thought of as functions, the group operation will be function composition, i.e., applying one permutation after another. Thus, Sn has order n!, which is the number of ways to permute the n integers. We will now introduce a very useful notation, known as cyclic notation, for ...
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Fisher–Yates shuffle



The Fisher–Yates shuffle (named after Ronald Fisher and Frank Yates), also known as the Knuth shuffle (after Donald Knuth), is an algorithm for generating a random permutation of a finite set—in plain terms, for randomly shuffling the set. A variant of the Fisher–Yates shuffle, known as Sattolo's algorithm, may be used to generate random cyclic permutations of length n instead. The Fisher–Yates shuffle is unbiased, so that every permutation is equally likely. The modern version of the algorithm is also rather efficient, requiring only time proportional to the number of items being shuffled and no additional storage space.Fisher–Yates shuffling is similar to randomly picking numbered tickets (combinatorics: distinguishable objects) out of a hat without replacement until there are none left.
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