Hostname: page-component-7d684dbfc8-d9hj2 Total loading time: 0 Render date: 2023-09-28T21:25:35.516Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "coreDisableSocialShare": false, "coreDisableEcommerceForArticlePurchase": false, "coreDisableEcommerceForBookPurchase": false, "coreDisableEcommerceForElementPurchase": false, "coreUseNewShare": true, "useRatesEcommerce": true } hasContentIssue false

The Hook Graphs of the Symmetric Group

Published online by Cambridge University Press:  20 November 2018

J. S. Frame
Michigan State College
G. de B. Robinson
University of Toronto
R. M. Thrall
University of Michigan
Rights & Permissions [Opens in a new window]


Core share and HTML view are not possible as this article does not have html 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.

Research Article
Copyright © Canadian Mathematical Society 1954


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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
12. Staal, R. A., Star diagrams and the symmetric group, Can. J. Math., 2 (1950), 79–92.CrossRefGoogle 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.CrossRefGoogle Scholar
14. Young, A., On quantitative substitutional analysis II, Proc. London Math. Soc, 34 (1902), 361–397.Google Scholar