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De Bruijn enumeration applied to some genetical problems

Published online by Cambridge University Press:  24 October 2008

E. Keith Lloyd
E. Keith Lloyd
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Southampton, United Kingdom, 809 5NH
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Extract

Several authors have considered relationships between individuals specified by the genes which they have in common, where two genes are regarded as the same if and only if they are identical by descent from some common ancestor. In particular Thompson [6] considered n pairs of genes, one pair from each of n individuals, and studied the number Nn of gene identity states, the number Mn, k of such states in which there are exactly k distinct genes and the number Dn of genetically distinct states (see Definitions 2 and 4 below). In this type of work the nature of the genes themselves is of no interest, but only which genes are identical to which, and precise definitions are best given in terms of orbits under group actions. Thompson did use some group theory in her work, but not the full machinery of Redfield-Pólya-de Bruijn enumeration.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 2 , March 1988 , pp. 277 - 284
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

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