Abstract
When A, B are sets, the set B A of all functions f: A → B is mentioned at various places throughout this book. We here intend to count it, when A, B are finite, and discuss its relationships with other sets, such as the set of all shuffles of A. Now, there are two useful general principles for counting a finite set X:
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(i)
we find a known set Y, already counted, and show that X ≈ Y;
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(ii)
we find some equivalence relation R on X, partition X into cosets mod R as in Theorem 4.5.12, count each coset, and add up; often the cosets all have the same number of elements.
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© 1970 H. B. Griffiths and P. J. Hilton
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Griffiths, H.B., Hilton, P.J. (1970). Sets of Functions. In: A Comprehensive Textbook of Classical Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6321-0_6
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DOI: https://doi.org/10.1007/978-1-4612-6321-0_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90342-2
Online ISBN: 978-1-4612-6321-0
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