Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-27T23:16:27.189Z Has data issue: false hasContentIssue false
  • English
  • Français

The Hook Graphs of the Symmetric Group

Published online by Cambridge University Press:  20 November 2018

J. S. Frame ,
G. de B. Robinson  and
R. M. Thrall
J. S. Frame
Affiliation:
Michigan State College
G. de B. Robinson
Affiliation:
University of Toronto
R. M. Thrall
Affiliation:
University of Michigan
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.

Each irreducible representation [λ] of the symmetric group Sn may be identified by a partition [λ] of n into non-negative integral parts λ1 ≥ λ2 ≥ … λn ≥ 0, of which the first λ'j parts are ≥j, or by a right (Young) diagram also called [λ], that contains λi nodes in its ith row and λ'j nodes in its jth column.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 316 - 324
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Brauer, R. and Robinson, G. de B., On a conjecture by Nakayama, Proc. Roy. Soc. Canada, Sec. III (3) 41 (1947), 11-19, 20–25.Google Scholar
2. Farahat, H., On p-quotients and star diagrams of the symmetric group, Proc. Cambridge Phil. Soc, 49 (1953), 157-160.Google Scholar
3. Frobenius, G., Ueber die Charaktere der symmetrischen Gruppe, Preuss. Akad. Wiss. Sitz., (1900), 516–534.Google Scholar
4. Frobenius, G., Ueber die charakteristischen Einheiten der symmetrischen Gruppe, ibid. (1903),328–358.Google Scholar
5. Littlewood, D. E., Modular representations of symmetric groups, Proc. Roy. Soc. London (A), 209 (1951), 333–352.Google Scholar
6. Murnaghan, F. D., Theory of group representations (Baltimore, 1938), 119.Google Scholar
7. Nakayama, T., Some modular properties of irreducible representations of a symmetric group I,II, Jap. J. Math., 17 (1941), 165–184, 277–294.Google Scholar
8. Nakayama, T. and Osima, M., Note on blocks of symmetric groups, Nagoya Math. J., 2 (1951), 111–117.Google Scholar
9. Robinson, G. de B., On the representations of the symmetric group III, Amer. J. Math., 70 (1948), 277–294.Google Scholar
10. Robinson, G. de B., On the modular representations of the symmetric group I, II, III, Proc. Nat. Acad. Sci., 37 (1951), 694–696, 88 (1952), 129–133, 424–426.Google Scholar
11. Robinson, G. de B., On a conjecture by J. H. Chung, Can. J. Math., 4 (1952), 373–380.Google Scholar
12. Staal, R. A., Star diagrams and the symmetric group, Can. J. Math., 2 (1950), 79–92.Google Scholar
13. Thrall, R. M. and Robinson, G. de B., Supplement to a paper by G. de B. Robinson, Amer. J. Math., 73 (1951), 721–724.Google Scholar
14. Young, A., On quantitative substitutional analysis II, Proc. London Math. Soc, 34 (1902), 361–397.Google Scholar