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On the Modular Representation of the Symmetric Group

  • G. De B. Robinson (a1)

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1. Introduction. It has been observed (2) that the number of p-regular classes of Sn, i.e. the number of classes of order prime to p, is equal to the number of partitions (λ) of n in which no summand is repeated p or more times. For this relation to hold it is essential that p be prime. It seems natural to call the Young diagram [λ] associated with (λ) p-regular if no p of its rows are of equal length, otherwise p-singular.

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References

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1. Farahat, H., On the representations of the symmetric group, Proc. London Math. Soc. (3), 4 (1954), 303316.
2. Frame, J. S. and Robinson, G. de B., On a theorem of Osima and Nagao, Can. J. Math., 6 (1954), 125127.
3. Frame, J. S., Robinson, G. de B. and Thrall, R. M., The hook graphs of the symmetric group, Can. J. Math., 6 (1954), 316324.
4. Nagao, H., Note on the modular representations of symmetric groups, Can. J. Math., 5 (1953), 356363.
5. Osima, M., Some remarks on the characters of the symmetric group, Can. J. Math., 5 (1953), 336343.
6. Osima, M., II, ibid., 6 (1954), 511–521.
7. Robinson, G. de B., On a conjecture by J. H. Chung, Can. J. Math., 4 (1952), 373380.
8. Robinson, G. de B., On the modular representations of the symmetric group IV, ibid., 6 (1954), 486–497.
9. Thrall, R. M. and Robinson, G. de B., Supplement to a paper by G. de B. Robinson, Amer. J. Math., 73 (1951), 721724.
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On the Modular Representation of the Symmetric Group

  • G. De B. Robinson (a1)

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