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Restricted Choices

Published online by Cambridge University Press:  20 November 2018

M. Abramson
M. Abramson*
Affiliation:
McGill University
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A subset consisting of k elements chosen, from n distinct ordered elements, with given restrictions is called are stricted choice. For example, one restriction on the k elements may be that no two consecutive elements appear, while another may be that no two alternate elements appear. Certain restricted choices may be used to obtain solutions to permutation problems ([1, p. 349]; [4]). Each restricted choice corresponds to a "restricted sequence of Bernoulli trials" as described in [1], In this paper an elementary method of obtaining more general types of restricted choices is given. Some special cases of the restricted choices and restricted Bernoulli trials are presented in the form of examples.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 5 , October 1965 , pp. 585 - 600
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Abramson, M., Explicit Expressions for a Class of Permutation Problems, Canada. Math. Bull., Vol. 7, No. 3, (1964), pp. 345-350.Google Scholar
2. Bhaskarandha, C.N., Solution of Problem E1485, Amer. Math. Monthly, Vol.69 (1962), p. 315.Google Scholar
3. Bizley, M. T. L., A Problem in Permutations, Amer. Math. Monthly, Vol.70(1963), pp. 722-730.Google Scholar
4. Kaplansky, I., Solution of the "Problème des Ménages", Bull. Amer. Math. Soc., Vol.49 (1943), pp. 784-785.Google Scholar