References
- [1]
-
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.
- [2]
-
L.E. Dickson.
Linear Groups.
Dover Publications, Inc., New York, 1958.
- [3]
-
B. Elspas.
The Theory of Autonomous Linear Sequential Networks.
IRE Transactions on Circuit Theory, CT-6:45 - 60, 1959.
- [4]
-
H. Fripertinger.
Cycle indices of linear, affine and projective groups.
To be published.
- [5]
-
J.A. Green.
The characters of the finite general linear groups.
Trans. Amer. Math. Soc., 80:402 - 447, 1955.
- [6]
-
J.W.P. Hirschfeld.
Projective Geometries over Finite Fields.
Clarendon Press, Oxford, 1979.
ISBN 0-19-853526-0.
- [7]
-
A. Kerber.
Algebraic Combinatorics via Finite Group Actions.
B. I. Wissenschaftsverlag, Mannheim, Wien, Zürich, 1991.
ISBN 3-411-14521-8.
- [8]
-
J.P.S. Kung.
The Cycle Structure of a Linear Transformation over a
Finite Field.
Linear Algebra and its Applications, 36:141 - 155, 1981.
- [9]
-
H. Lehmann.
Das Abzähltheorem der Exponentialgruppe in gewichteter Form.
Mitteilungen aus dem Mathem. Seminar Giessen, 112:19 - 33,
1974.
- [10]
-
H. Lehmann.
Ein vereinheitlichender Ansatz für die REDFIELD -
PÓLYA - de BRUIJNSCHE Abzähltheorie.
PhD thesis, Universität Giessen, 1976.
- [11]
-
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.
- [12]
-
G. Pólya.
Kombinatorische Anzahlbestimmungen für
Gruppen, Graphen und chemische Verbindungen.
Acta Mathematica, 68:145 - 254, 1937.
- [13]
-
D. Slepian.
Some Further Theory of Group Codes.
The Bell System Technical Journal, 39:1219 - 1252, 1960.
- [14]
-
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