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Computations of the partition function

Published online by Cambridge University Press:  01 August 2016

P. Shiu
P. Shiu*
Affiliation:
Department of Mathematical Sciences, Loughborough University, Leicestershire LE11 3TU
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Extract

How many ways are there of making up £1 using coins? Omitting the use of the £1 coin, we are asking for the number of ways of ‘partitioning’ 100 using parts of 1, 2, 5, 10, 20, 50. For n ≥ 0, let f (n) denote the number of solutions to the equation

in non-negative integers xi, so that our required number is f (100). It is not difficult to see that f(n) is the coefficient of tn in the product Π(1 + tk + t2k +… ) over the parts k = 1, 2, 5, 10, 20, 50.

Type
Articles
Information
The Mathematical Gazette , Volume 81 , Issue 490 , March 1997 , pp. 45 - 52
Copyright
Copyright © The Mathematical Association 1997

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References

1. Shiu, CM. and Shiu, P., Stamps and coins: two partition problems, Mathematical Spectrum, 13, (1981) pp. 49–55.Google Scholar
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