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Number of Arrangements

Published online by Cambridge University Press:  03 November 2016

E. M. Wright
E. M. Wright*
Affiliation:
University of Aberdeen
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Extract

In a recent article [1] in this Gazette, Collings discusses the number of arrangements of n railway trucks on k sidings under a variety of conditions. Let qk (n) be the number of ways of arranging n indistinguishable trucks on k indistinguishable sidings or, what is the same thing, the number of partitions of n into not more than k parts. Let pk (n) be the number of these arrangements which use all k sidings, that is, the number of partitions of n into exactly k parts. Collings describes the determination of pk(n) and qk(n) as an unsolved problem in partition theory; this is not quite correct.

Type
Research Article
Information
The Mathematical Gazette , Volume 51 , Issue 378 , December 1967 , pp. 305 - 308
Copyright
Copyright © Mathematical Association 1931

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References

1. Collings, S. N., Math. Gaz. 50 (1966), 287–289.CrossRefGoogle Scholar
2. Euler, L., Introducilo in analysin inflnitorum I (1747) (Lausanne 1747), cap. 16; Opera omnia (I) (Leipzig 1922) VIII, 313–338.Google Scholar
3. Glaisher, J. W. L. Quart. J. Math. 40 (1909), 275–348.Google Scholar
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