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The expected number of people needed until every birthday is achieved is called the Coupon collector's problem. It can be calculated by nH n, where H n is the n th harmonic number. For 365 possible dates (the birthday problem), the answer is 2365.
The name is based on the birthday paradox. Choose m birthdays in a year of n days. List the spacings between the birthdays. If j is the number of values that occur more than once in that list, then j is asymptotically Poisson-distributed with mean m 3 / (4n).
Toggle Permutation groups and other algebraic structures subsection. 3.1 Groups. 3.2 Other algebraic structures. ... 6 Number theory. 7 Algorithms and information ...
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 ...
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In a 1977 review of permutation-generating algorithms, Robert Sedgewick concluded that it was at that time the most effective algorithm for generating permutations by computer. [2] The sequence of permutations of n objects generated by Heap's algorithm is the beginning of the sequence of permutations of n+1 objects.
The sum of the numbers in the factorial number system representation gives the number of inversions of the permutation, and the parity of that sum gives the signature of the permutation. Moreover, the positions of the zeroes in the inversion table give the values of left-to-right maxima of the permutation (in the example 6, 8, 9) while the ...
Merge sort. In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order.The most frequently used orders are numerical order and lexicographical order, and either ascending or descending.