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A045923
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Number of irreducible representations of symmetric group S_n for which every matrix has determinant 1.
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0
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1, 1, 1, 2, 2, 7, 7, 10, 10, 34, 40, 53, 61, 103, 112, 143, 145, 369, 458, 579, 712, 938, 1127, 1383, 1638, 2308, 2754, 3334, 3925, 5092
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OFFSET
| 1,4
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COMMENTS
| Irreducible representations of S_n contained in the special linear group were first considered by L. Solomon (unpublished).
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REFERENCES
| R. P. Stanley, Enumerative Combinatorics, vol. 2, Cambridge University Press, Cambridge and New York, 1999, Exercise 7.55.
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EXAMPLE
| a(5)=2, since only the irreducible representations indexed by the partitions (5) and (3,2) are contained in the special linear group
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CROSSREFS
| Sequence in context: A064288 A054085 A021443 * A199886 A117779 A195326
Adjacent sequences: A045920 A045921 A045922 * A045924 A045925 A045926
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KEYWORD
| nonn,nice
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AUTHOR
| R. P. Stanley (rstan(AT)math.mit.edu)
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