Abstract
It is a well-known problem to find for n letters the number of the arrangements in which no letter occupies its original place; and the solution of it is given by the following general theorem :— viz., the number of the arrangements which satisfy any r conditions iswhere 1 denotes the whole number of arrangements; (1) the number of them which fail in regard to the first condition; (2) the number which fail in regard to the second condition; (12) the number which fail in regard to the first condition, and also in regard to the second condition; and so on: Σ(1) means (1) + (2) … + (r) : Σ(12) means (12) + (13) + (2r) … + (r − 1, r); and so on, up to (12…r), which denotes the number failing in regard to each of the r conditions.
Publisher
Cambridge University Press (CUP)
Subject
General Medicine,General Chemistry
Cited by
8 articles.
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1. 102.18 The problème des ménages revisited;The Mathematical Gazette;2018-02-08
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5. Sequences of Integers;Unsolved Problems in Number Theory;1994