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References

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N.G. De Bruijn. Pólya's Theory of Counting. In E.F. Beckenbach, editor, Applied Combinatorial Mathematics, chapter 5, pages 144 - 184. Wiley, New York, 1964.
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L.E. Dickson. Linear Groups. Dover Publications, Inc., New York, 1958.
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B. Elspas. The Theory of Autonomous Linear Sequential Networks. IRE Transactions on Circuit Theory, CT-6:45 - 60, 1959.
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H. Fripertinger. Cycle indices of linear, affine and projective groups. To be published.
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J.A. Green. The characters of the finite general linear groups. Trans. Amer. Math. Soc., 80:402 - 447, 1955.
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J.W.P. Hirschfeld. Projective Geometries over Finite Fields. Clarendon Press, Oxford, 1979. ISBN 0-19-853526-0.
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A. Kerber. Algebraic Combinatorics via Finite Group Actions. B. I. Wissenschaftsverlag, Mannheim, Wien, Zürich, 1991. ISBN 3-411-14521-8.
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J.P.S. Kung. The Cycle Structure of a Linear Transformation over a Finite Field. Linear Algebra and its Applications, 36:141 - 155, 1981.
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H. Lehmann. Das Abzähltheorem der Exponentialgruppe in gewichteter Form. Mitteilungen aus dem Mathem. Seminar Giessen, 112:19 - 33, 1974.
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H. Lehmann. Ein vereinheitlichender Ansatz für die REDFIELD - PÓLYA - de BRUIJNSCHE Abzähltheorie. PhD thesis, Universität Giessen, 1976.
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R. Lidl and H. Niederreiter. Finite Fields, volume 20 of Encyclopedia of Mathematics and its Applications. Addison-Wesley Publishing Company, London, Amsterdam, Don Mills - Ontario, Sydney, Tokyo, 1983. ISBN 0-201-13519-1.
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G. Pólya. Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen. Acta Mathematica, 68:145 - 254, 1937.
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D. Slepian. Some Further Theory of Group Codes. The Bell System Technical Journal, 39:1219 - 1252, 1960.
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St. Weinrich. Konstruktionsalgorithmen für diskrete Strukturen und ihre Implementierung. Master's thesis, Universität Bayreuth, July 1993.

Rnk2
n\k 1 2 3 4 5 6 7 8 9 10
1 1 0 0 0 0 0 0 0 0 0
2 1 0 0 0 0 0 0 0 0 0
3 1 1 0 0 0 0 0 0 0 0
4 1 1 1 0 0 0 0 0 0 0
5 1 2 2 1 0 0 0 0 0 0
6 1 3 5 3 1 0 0 0 0 0
7 1 4 10 10 4 1 0 0 0 0
8 1 5 18 28 18 5 1 0 0 0
9 1 7 31 71 71 31 7 1 0 0
10 1 8 51 165 250 165 51 8 1 0
11 1 10 79 361 809 809 361 79 10 1
12 1 12 121 754 2484 3759 2484 754 121 12

Rnk3
n\k 1 2 3 4 5 6 7
1 1 0 0 0 0 0 0
2 1 0 0 0 0 0 0
3 1 1 0 0 0 0 0
4 1 2 1 0 0 0 0
5 1 3 3 1 0 0 0
6 1 5 10 5 1 0 0
7 1 7 24 24 7 1 0
8 1 10 55 105 55 10 1
9 1 13 116 403 403 116 13
10 1 17 231 1506 3000 1506 231
11 1 21 438 5425 23579 23579 5425
12 1 27 813 19440 199473 469473 199473

Rnk4
n\k 1 2 3 4 5 6 7
1 1 0 0 0 0 0 0
2 1 0 0 0 0 0 0
3 1 1 0 0 0 0 0
4 1 2 1 0 0 0 0
5 1 4 4 1 0 0 0
6 1 6 14 6 1 0 0
7 1 9 38 38 9 1 0
8 1 13 104 238 104 13 1
9 1 18 276 1573 1573 276 18
10 1 25 711 11566 34288 11566 711
11 1 32 1793 88140 909664 909664 88140
12 1 42 4446 665736 25.020688 90.186547 25.020688

Rnk5
n\k 1 2 3 4 5 6
1 1 0 0 0 0 0
2 1 0 0 0 0 0
3 1 1 0 0 0 0
4 1 2 1 0 0 0
5 1 4 4 1 0 0
6 1 8 18 8 1 0
7 1 11 62 62 11 1
8 1 18 222 659 222 18
9 1 26 800 8232 8232 800
10 1 38 2805 117351 483955 117351
11 1 51 9642 1674434 32.156437 32.156437

Rnk7
n\k 1 2 3 4 5
1 1 0 0 0 0
2 1 0 0 0 0
3 1 1 0 0 0
4 1 3 1 0 0
5 1 5 5 1 0
6 1 11 32 11 1
7 1 18 165 165 18
8 1 33 1006 4741 1006
9 1 50 6362 179586 179586
10 1 83 39417 7.058258 45.507354
11 1 123 233578 260.571116 11419.262502

This paper was published in: Lecture Notes in Computer Science 948, Applied Algebra, Algebraic Combinatorics, Error Correcting Codes, 11th International Symposion, AAECC-11, G. Cohen, M. Giusti and T. Mora (eds.), Springer, (1995), 194 - 204.


harald.fripertinger@kfunigraz.ac.at,
last changed: January 23, 2001

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