Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

A General Class of Enumerations Arising in Genetics

J. H. Bennett
Biometrics
Vol. 23, No. 3 (Sep., 1967), pp. 517-537
DOI: 10.2307/2528012
Stable URL: http://www.jstor.org/stable/2528012
Page Count: 21
  • Read Online (Free)
  • Download ($14.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A General Class of Enumerations Arising in Genetics
Preview not available

Abstract

Fisher [1950] gave a general combinatorial method of solution for a class of enumerations in genetics where one is concerned with sets of formulae generated by a given permutation group. As similar problems arise in fields other than genetics, Fisher's enumerations seem to deserve wider attention than they have received. One series of expressions giving the number of partitions of an integer n in k dimensions (or equally the number of sets of isomorphic n-somic genotypes heterogenic at k linked loci) appears to be of very general interest. Foulkes [1965], using group representation theory, has shown that further analysis of Fisher's enumerations is possible in terms of subgroups of the basic permutation group and he has raised the question as to how these subgroups enter into the genetical problems. This article shows how, using an extension of Fisher's method, the subgroups to which Foulkes has drawn attention arise naturally in the genetical context. The enumerations given by Foulkes refer to sets of genetical formulae which are invariant under various subgroups of permutations.

Page Thumbnails

  • Thumbnail: Page 
517
    517
  • Thumbnail: Page 
518
    518
  • Thumbnail: Page 
519
    519
  • Thumbnail: Page 
520
    520
  • Thumbnail: Page 
521
    521
  • Thumbnail: Page 
522
    522
  • Thumbnail: Page 
523
    523
  • Thumbnail: Page 
524
    524
  • Thumbnail: Page 
525
    525
  • Thumbnail: Page 
526
    526
  • Thumbnail: Page 
527
    527
  • Thumbnail: Page 
528
    528
  • Thumbnail: Page 
529
    529
  • Thumbnail: Page 
530
    530
  • Thumbnail: Page 
531
    531
  • Thumbnail: Page 
532
    532
  • Thumbnail: Page 
533
    533
  • Thumbnail: Page 
534
    534
  • Thumbnail: Page 
535
    535
  • Thumbnail: Page 
536
    536
  • Thumbnail: Page 
537
    537