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A000637 Number of fixed-point-free permutation groups of degree n.
(Formerly M1730 N0685)
12
1, 0, 1, 2, 7, 8, 37, 40, 200, 258, 1039, 1501, 7629, 10109, 54322, 83975, 527036, 780193, 5808293 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
a(1) = 0 since the trivial group of degree 1 has a fixed point. One could also argue that one should set a(1) = 1 by convention.
REFERENCES
G. Butler and J. McKay, The transitive groups of degree up to eleven, Comm. Algebra, 11 (1983), 863-911.
D. Holt, Enumerating subgroups of the symmetric group. Computational Group Theory and the Theory of Groups, II, edited by L.-C. Kappe, A. Magidin and R. Morse. AMS Contemporary Mathematics book series, vol. 511, pp. 33-37.
A. Hulpke, Konstruktion transitiver Permutationsgruppen, Dissertation, RWTH Aachen, 1996.
A. Hulpke, Constructing transitive permutation groups, J. Symbolic Comput. 39 (2005), 1-30.
A. Hulpke, Constructing Transitive Permutation Groups, in preparation
C. C. Sims, Computational methods in the study of permutation groups, pp. 169-183 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
G. Butler and J. McKay, The transitive groups of degree up to eleven, Comm. Algebra, 11 (1983), 863-911. [Annotated scanned copy]
D. Holt, Enumerating subgroups of the symmetric group, in Computational Group Theory and the Theory of Groups, II, edited by L.-C. Kappe, A. Magidin and R. Morse. AMS Contemporary Mathematics book series, vol. 511, pp. 33-37. [Annotated copy]
A. C. Lunn and J. K. Senior, Isomerism and Configuration, J. Physical Chem. 33 (7) 1929, 1027-1079.
A. C. Lunn and J. K. Senior, Isomerism and Configuration, J. Physical Chem. 33 (7) 1929, 1027-1079. [Annotated scan of page 1069 only]
FORMULA
a(n) = A000638(n) - A000638(n-1). - Christian G. Bower, Feb 23 2006
CROSSREFS
Cf. A000019, A002106. Unlabeled version of A116693.
Sequence in context: A081700 A093795 A001493 * A250715 A198322 A222134
KEYWORD
nonn,hard,more,nice
AUTHOR
EXTENSIONS
More terms from Alexander Hulpke
a(2) and a(10) corrected, a(11) and a(12) added by Christian G. Bower, Feb 23 2006
Terms a(13)-a(18) were computed by Derek Holt and contributed by Alexander Hulpke. Jul 30 2010, who comments that he has verified the terms up through a(16).
Edited by N. J. A. Sloane, Jul 30 2010, at the suggestion of Michael Somos
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)