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Some Remarks on the Characters of the Symmetric Group, II

Published online by Cambridge University Press:  20 November 2018

Masaru Osima*
Affiliation:
Okayama University
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Let p be a fixed prime number. We denote by k(n) the number of partitions of n. As is well known, the number of ordinary irreducible characters of the symmetric group Sn is k(n). We set k(0)=1.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Brauer, R. and Nesbitt, C., On the modular characters of groups, Ann. of Math., 42 (1941), 556–590.Google Scholar
2. Brauer, R. and Robinson, G. de B., On the conjecture by Nakayama, Trans. Royal Soc. Canada, Series III, Sec. III , 40 (1947), 11–25.Google Scholar
3. Chung, J. H., Modular representations of the symmetric group, Can. J. Math., 3 (1951), 309–327.Google Scholar
4. Farahat, H., On p-quotients and star diagrams of the symmetric group, Proc. Camb. Phil. Soc, 49 (1953), 157–160.Google Scholar
4a. Frame, J. S. and Robinson, G. de B., On a theorem of Osima and Nagao, Can. J. Math., 6 (1954), 125–127.Google Scholar
5. Littlewood, D. E., The theory of group characters (Oxford, 1950).Google Scholar
6. Littlewood, D. E., Modular representations of symmetric groups, Proc. Roy. Soc. A, 209 (1951), 333–353.Google Scholar
7. Murnaghan, F. D., On the representations of the symmetric group, Amer. J. Math., 59 (1937), 437–488.Google Scholar
8. H. Nagao, , Note on the modular representations of symmetric groups, Can. J. Math., 5 (1953), 356–363.Google Scholar
9. Nakayama, T., On some modular properties of irreducible representations of a symmetric group I, Jap. J. Math., 17 (1941), 89–108.Google Scholar
10. Nakayama, T., II, ibid., 411–423.Google Scholar
11. Nakayama, T. and Osima, M., Note on blocks of symmetric groups, Nagoya Math. J., 2 (1951), 111–117.Google Scholar
12. Osima, M., On some character relations of symmetric groups, Math. J. Okayama Univ., 1 (1952), 63–68.Google Scholar
13. Osima, M., Some remarks on the characters of the symmetric group, Can. J. Math., 5 (1953), 336–343.Google Scholar
13a. Osima, M., On the representations of the generalized symmetric group, Math. J. Okayama University, 4 (1954), to appear.Google Scholar
14. Robinson, G. de B., On the representations of the symmetric group III, Amer. J. Math., 70 (1948), 277–294.Google Scholar
15. Robinson, G. de B., On the modular representations of the symmetric group, Proc. Nat. Acad. Sci. U.S.A., 87 (1951), 694–696.Google Scholar
16. Robinson, G. de B., On a conjecture by J. H. Chung, Can. J. Math., 4 (1952), 373–380.Google Scholar
17. Staal, R. A., Star diagrams and the symmetric group, Can. J. Math., 2 (1950), 79–92.Google Scholar
18. Thrall, R. M. and Robinson, G. de B., Supplement to a paper of G. de B. Robinson, Amer. J. Math., 73 (1951), 721–724 Google Scholar