Hostname: page-component-7479d7b7d-rvbq7 Total loading time: 0 Render date: 2024-07-11T06:23:13.769Z Has data issue: false hasContentIssue false
  • English
  • Français

Special train algebras arising in genetics II

Published online by Cambridge University Press:  20 January 2009

Harry Gonshor
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We shall extend some of the results of (7) to the case of multiple alleles, our primary concern being that of polyploidy combined with multiple alleles. Generalisations often tend to make the computations more involved as is expected. Fortunately here, the attempt to generalise has led to a new method which not only handles the case of multiple alleles, but is an improvement over the method used in (7) for the special case of polyploidy with two alleles. This method which consists essentially of expressing certain elements of the algebra in a so-called “ factored ” form, gives greater insight into the structure of a polyploidy algebra, and avoids a great deal of the computation with binomial coefficients, e.g. see (7), p. 46.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 14 , Issue 4 , December 1965 , pp. 333 - 338
Copyright
Copyright © Edinburgh Mathematical Society 1965

References

REFERENCES

(1) Etherington, I. M. H., Genetic algebras. Proc. Roy. Soc. Edin. 59 (1939), 242–258.CrossRefGoogle Scholar
(2) Etherington, I. M. H., Commutative train algebras of ranks 2 and 3. J. London Math. Soc. 15 (1940), 136–149; 20 (1945), 238.CrossRefGoogle Scholar
(3) Etherington, I. M. H., Special train algebras. Quart. J. Math. (Oxford), 12 (1941), 1–8.Google Scholar
(4) Etherington, I. M. H., Non-associative algebra and the symbolism of genetics, Proc. Roy. Soc. Edin. B, 61 (1941), 24–42.Google Scholar
(5) Etherington, I. M. H., Duplication of linear algebras. Proc. Edin. Math. Soc. (2) 6 (1941), 222–230.CrossRefGoogle Scholar
(6) Etherington, I. M. H., Non-commutative train algebras of ranks 2 and 3. Proc. London Math. Soc. (2) 52 (1951), 241–252.Google Scholar
(7) GONSHOR, H., Special train algebras arising in genetics. Proc. Edin. Math. Soc. (2) 12 (1960), 41–53.CrossRefGoogle Scholar
(8) Rafftn, R., Axiomatisation des algebres genetiques. Acad. Roy. Belgique Bull. Cl. Sci. (5) 37 (1951), 359–366.Google Scholar
(9) Reiersol, O., Genetic algebras studied recursively and by means of differential operators. Math. Scand. 10 (1962), 25–44.CrossRefGoogle Scholar
(10) Schafer, R. D., Structure of genetic algebras, Amer. J. Math. 71 (1949), 121–135.CrossRefGoogle Scholar