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How many dead ends in a derangement?

Published online by Cambridge University Press:  23 January 2015

Barry Lewis
Barry Lewis*
Affiliation:
110 Highgate Hill, London N6 5HE
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Extract

This article is concerned with two sequences and the matrices they induce. The first, the Derangement sequence is well known to readers of the Gazette. It has been written about and its properties derived in many ways and on many previous occasions [1 – 11]. In contrast the second sequence, the Deadend sequence, is not well known – and certainly not the name since I made that up while writing this article. However, I want to explore these sequences in a single, systematic way. For the former it gives a fresh account of its properties, and for the latter it sets out corresponding results. The surprise is that they tum out to be closely related; surprising since their very different definitions mask such a connection. More than this, most of these properties may be established in the most fundamental way, based on elegant enumerative arguments. So they are free of specialised expertise or technique and may be enjoyed just as they are.

Type
Articles
Information
The Mathematical Gazette , Volume 97 , Issue 538 , March 2013 , pp. 81 - 94
Copyright
Copyright © The Mathematical Association 2013

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References

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