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Search: id:A059867
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| A059867 |
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Number of irreducible representations of the symmetric group S_n that have odd degree. |
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8
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| 1, 2, 2, 4, 4, 8, 8, 8, 8, 16, 16, 32, 32, 64, 64, 16, 16, 32, 32, 64, 64, 128, 128, 128, 128, 256, 256, 512, 512, 1024, 1024, 32, 32, 64, 64, 128, 128, 256, 256, 256, 256, 512, 512, 1024, 1024, 2048, 2048, 512, 512, 1024, 1024, 2048, 2048, 4096, 4096, 4096, 4096
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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John McKay, Irreducible representations of odd degree, Journal of Algebra 20, 1972 pages 416-418.
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FORMULA
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If n = sum 2^e[i] in binary, then the number of odd degree irreducible complex representations of S_n is 2^sum e[i]. In words: write n in binary and take the product of the powers of 2 that appear.
G.f.: prod(k>=0, 1 + 2^k * x^2^k). a(n) = 2^A073642(n). - Ralf Stephan, Jun 02 2003
a(1)=1, a(2n) = 2^e1(n)*a(n), a(2n+1) = a(2n), where e1(n) = A000120(n). - Ralf Stephan, Jun 19 2003
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EXAMPLE
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a(3) = 2 because S_3 the degrees of the irreducible representations of S_3 are 1,1,2.
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CROSSREFS
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Cf. A029930, A029931, A073642.
Sequence in context: A138219 A100835 A120541 this_sequence A046971 A051754 A108747
Adjacent sequences: A059864 A059865 A059866 this_sequence A059868 A059869 A059870
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KEYWORD
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nonn,easy
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AUTHOR
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Noam Katz (noamkj(AT)hotmail.com), Feb 28 2001
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Mar 27 2001
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