Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T00:40:58.906Z Has data issue: false hasContentIssue false
  • English
  • Français

Special Train Algebras Arising in Genetics

Published online by Cambridge University Press:  20 January 2009

H. Gonshor
H. Gonshor
Affiliation:
Mathematics Department, Rutgers University, New Brunswick, N.J., U.S.A.
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.

Ever since Mendel promulgated his famous laws, probability theory and statistics have played an important role in the study of heredity (9). Etherington introduced some concepts of modern algebra when he showed how a nonassociative algebra can be made to correspond to a given genetic system (1, 4). The fact that many of these algebras have common properties has led to their study from a purely abstract point of view (2, 3, 5, 6, 11, 12). Furthermore, the techniques of algebra give new ways of attacking problems in genetics such as that of stability.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 12 , Issue 1 , June 1960 , pp. 41 - 53
Copyright
Copyright © Edinburgh Mathematical Society 1960

References

REFERENCES

(1)Ethertngton, 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.CrossRefGoogle 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)Geiringer, H., On some mathematical problems arising in the development of Mendelian genetics, J. Amer. Stat. Assoc, 44 (1949), 526–547.CrossRefGoogle ScholarPubMed
(8)Haldane, J. B. S., Theoretical genetics of autopolyploids, J. Genetics, 22 (1930), 359–372.CrossRefGoogle Scholar
(9)Jennings, H. S., The numerical results of diverse systems of breeding, Genetics, 1 (1916), 53–89.CrossRefGoogle ScholarPubMed
(10)Knopp, K., Theory and Application of Infinite Series (Blackie), 1928.Google Scholar
(11)Raffin, R., Axiomatisation des algèbres génétiques, Acad. Roy. BelgiqueBull. Cl. Sci.(5), 37 (1951), 359–366.Google Scholar
(12)Schafer, R. D., Structure of genetic algebras, Amer. J. Math., 71 (1949), 121–135.CrossRefGoogle Scholar