Abstract
The set of the permutations of degree having only cycles with lengths in a fixed set is investigated. The set is distinguished in the set of all positive integers by imposing certain number-theoretic conditions. The following assertions are proved.1) If is the cardinality of the finite set , then there exist positive constants and with such that 2) If the uniform probability distribution is introduced on the finite set and if is the number of cycles in a random permutation in , then the random variable is asymptotically normal with parameters 0 and 1 as .Bibliography: 4 titles.
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