cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A000637 Number of fixed-point-free permutation groups of degree n.

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%I A000637 M1730 N0685 #57 Aug 17 2025 21:11:10
%S A000637 1,0,1,2,7,8,37,40,200,258,1039,1501,7629,10109,54322,83975,527036,
%T A000637 780193,5808293
%N A000637 Number of fixed-point-free permutation groups of degree n.
%C A000637 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.
%D A000637 G. Butler and J. McKay, The transitive groups of degree up to eleven, Comm. Algebra, 11 (1983), 863-911.
%D A000637 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.
%D A000637 A. Hulpke, Konstruktion transitiver Permutationsgruppen, Dissertation, RWTH Aachen, 1996.
%D A000637 A. Hulpke, Constructing transitive permutation groups, J. Symbolic Comput. 39 (2005), 1-30.
%D A000637 A. Hulpke, Constructing Transitive Permutation Groups, in preparation
%D A000637 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.
%D A000637 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000637 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000637 G. Butler and J. McKay, <a href="/A000637/a000637_1.pdf">The transitive groups of degree up to eleven</a>, Comm. Algebra, 11 (1983), 863-911. [Annotated scanned copy]
%H A000637 D. Holt, <a href="/A000019/a000019_1.pdf">Enumerating subgroups of the symmetric group</a>, 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]
%H A000637 A. Hulpke, <a href="http://www.math.colostate.edu/~hulpke/smalldeg.html">Transitive groups of small degree</a>
%H A000637 A. C. Lunn and J. K. Senior, <a href="http://dx.doi.org/10.1021/j150301a009">Isomerism and Configuration</a>, J. Physical Chem. 33 (7) 1929, 1027-1079.
%H A000637 A. C. Lunn and J. K. Senior, <a href="/A000637/a000637.pdf">Isomerism and Configuration</a>, J. Physical Chem. 33 (7) 1929, 1027-1079. [Annotated scan of page 1069 only]
%H A000637 C. C. Sims, <a href="/A000019/a000019.pdf">Letter to N. J. A. Sloane (no date)</a>
%H A000637 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F A000637 a(n) = A000638(n) - A000638(n-1). - _Christian G. Bower_, Feb 23 2006
%Y A000637 Cf. A000001, A000019, A000638, A002106, A005432, A005226.
%Y A000637 Cf. A000019, A002106. Unlabeled version of A116693.
%K A000637 nonn,hard,more,nice
%O A000637 0,4
%A A000637 _N. J. A. Sloane_
%E A000637 More terms from _Alexander Hulpke_
%E A000637 a(2) and a(10) corrected, a(11) and a(12) added by _Christian G. Bower_, Feb 23 2006
%E A000637 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).
%E A000637 Edited by _N. J. A. Sloane_, Jul 30 2010, at the suggestion of _Michael Somos_