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Difference equations, determinants and the Secret Santa problem

Published online by Cambridge University Press:  01 August 2016

Tony Ward
Tony Ward*
Affiliation:
19 Woodside Close, Surbiton KT5 9JU
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Extract

In [1] it is shown that every second-order linear difference equation with, in general, variable coefficients can be reduced to the form

It is also shown that (1) can be solved explicitly provided that a particular solution a (n) of the ‘auxiliary equation’

can be found, and many cases in which a solution of (2) is available are discussed. However, [1] is defective in that no method of finding a solution of (2) in the general case is given.

Type
Articles
Information
The Mathematical Gazette , Volume 89 , Issue 514 , March 2005 , pp. 2 - 6
Copyright
Copyright © The Mathematical Association 2005

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References

1. Ward, A.J.B., The solution of finite difference equations, Math. Gaz. 82 (July 1998) pp. 215–224.Google Scholar
2. Krasopoulos, P.T., A comment on the solution of finite difference equations, Math. Gaz. 86 (July 2002) pp. 277–279.Google Scholar
3. McGuire, K.M., Mackiw, G. and Morrell, C.H., The Secret Santa problem, Math. Gaz. 83 (November 1999) pp. 467–472.Google Scholar
4. Gerrish, F. and Ward, A.J.B., Derangements and determinants, Math. Gaz. 57 (October 1973) pp. 209–211.Google Scholar
5. Horn, R.A. and Johnson, C.R., Matrix Analysis, Cambridge University Press (1985).Google Scholar