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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
4. Gupta, H. Gwyther, C. E. and Miller, J. C. P. Tables of Partitions (Royal Soc. Math. Tables 4, Cambridge 1958).Google Scholar
5. Rieger, G. J., Math. Ann. 138 (1959), 356–362.Google Scholar
6. Sylvester, J. J. Amer. J. Math. 5 (1882), 119–136.Google Scholar
7. Wright, E. M. Math. Annalen 142 (1961), 311–316.Google Scholar