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Search: id:A049314
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| A049314 |
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The number k(GL(n,q)) of conjugacy classes in GL(n,q), q=4. |
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+0
6
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| 3, 15, 60, 252, 1005, 4080, 16305, 65460, 261828, 1048260, 4192980, 16775955, 67103520, 268430160, 1073720415, 4294945932, 17179782540, 68719391100, 274877559420, 1099511281260, 4398045120300, 17592184654365
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Bound: k(GL(n,q))<q^n. Asymptotics: k(GL(n,q)~q^n as n tends to infinity.
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REFERENCES
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W. Feit and N. J. Fine, Pairs of commuting matrices over a finite field. Duke Math. Journal, 27 (1960) 91-94.
V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
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FORMULA
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The number a(n) of conjugacy classes in the group GL(n, q) is the coefficient of t^n in the infinite product: product k=1, 2, ... (1-t^k)/(1-qt^k) - Noam Katz (noamkj(AT)hotmail.com), Mar 30 2001.
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PROGRAM
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(MAGMA) [ NumberOfClasses(GL(n, 4)) : n in [1..8] ]; - from Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
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CROSSREFS
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Cf. A006951, A006952, A049315, A049316.
Sequence in context: A122597 A036750 A058748 this_sequence A001655 A128237 A058749
Adjacent sequences: A049311 A049312 A049313 this_sequence A049315 A049316 A049317
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu)
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