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.

Showing 1-10 of 10 results.

A263840 Erroneous version of A004027.

Original entry on oeis.org

1, 2, 13, 73, 710, 6079, 85311
Offset: 0

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Author

Keywords

Links

A004029 Number of n-dimensional space groups.

Original entry on oeis.org

1, 2, 17, 219, 4783, 222018, 28927915
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Right border of A293060. - Andrey Zabolotskiy, Oct 07 2017

References

  • H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space. Wiley, NY, 1978, p. 52.
  • P. Engel, Geometric crystallography, in P. M. Gruber and J. M. Wills, editors, Handbook of Convex Geometry. North-Holland, Amsterdam, Vol. B, pp. 989-1041.
  • J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 102 and 934.
  • T. Janssen, Crystallographic Groups. North-Holland, Amsterdam, 1973, p. 119.
  • R. L. E. Schwarzenberger, N-Dimensional Crystallography. Pitman, London, 1980, p. 34.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A006227, A004027, A293060.

Extensions

a(6) corrected by W. Plesken and T. Schulz. Thanks to Max Horn for reporting this correction, Dec 18 2009

A006226 Number of abstract n-dimensional crystallographic point groups.

Original entry on oeis.org

1, 2, 9, 18, 118, 239, 1594
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • P. Engel, "Geometric crystallography," in P. M. Gruber and J. M. Wills, editors, Handbook of Convex Geometry. North-Holland, Amsterdam, Vol. B, pp. 989-1041.
  • T. Janssen, Crystallographic Groups. North-Holland, Amsterdam, 1973, p. 73.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A004027, A004028, A004029.

Extensions

Two more terms from W. Plesken and T. Schulz (tilman(AT)momo.math.rwth-aachen.de), Feb 27 2001
Offset corrected by Andrey Zabolotskiy, Jul 10 2017

A006227 Number of n-dimensional space groups (including enantiomorphs).

Original entry on oeis.org

1, 2, 17, 230, 4894, 222097
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Right border of A293061. - Andrey Zabolotskiy, Oct 07 2017

References

  • Colin Adams, The Tiling Book, AMS, 2022; see p. 59.
  • H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space. Wiley, NY, 1978, p. 52.
  • P. Engel, Geometric crystallography, in P. M. Gruber and J. M. Wills, editors, Handbook of Convex Geometry. North-Holland, Amsterdam, Vol. B, pp. 989-1041.
  • J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 102.
  • T. Janssen, Crystallographic Groups. North-Holland, Amsterdam, 1973, p. 119.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A004027, A004029, A293061.

Extensions

a(4) corrected according to Neubüser, Souvignier and Wondratschek (2002) - Susanne Wienand, May 19 2014
a(5) added according to Souvignier (2003); a(6) should not be extracted from that paper because it uses the old incorrect CARAT data for d=6 - Andrey Zabolotskiy, May 19 2015

A004028 Number of geometric n-dimensional crystal classes.

Original entry on oeis.org

1, 2, 10, 32, 227, 955, 7103
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Number of Q-classes of finite subgroups of GL_n(Z) up to conjugacy.
Number of n-dimensional crystallographic point groups (not counting enantiomorphs). - Andrey Zabolotskiy, Jul 08 2017

References

  • H. Brown, R. Bülow, J. Neubüser, H. Wondratschek, and H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space. Wiley, NY, 1978, p. 52.
  • P. Engel, "Geometric crystallography," in P. M. Gruber and J. M. Wills, editors, Handbook of Convex Geometry. North-Holland, Amsterdam, Vol. B, pp. 989-1041.
  • T. Janssen, Crystallographic Groups. North-Holland, Amsterdam, 1973, p. 73.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A004027, A004029.

Extensions

a(6) corrected from CARAT page by D. S. McNeil, Jan 02 2011

A004032 Number of n-dimensional crystal families.

Original entry on oeis.org

1, 1, 4, 6, 23, 32, 91
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space. Wiley, NY, 1978, p. 52.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A004027-A004031, A006226, A006227.

Extensions

a(5)-a(6) from Henry Bottomley, Feb 03 2014

A059104 Number of Bieberbach groups in dimension n: torsion-free crystallographic groups.

Original entry on oeis.org

1, 2, 10, 74, 1060, 38746
Offset: 1

Views

Author

Tilman Schulz (tilman(AT)momo.math.rwth-aachen.de), Feb 13 2001

Keywords

References

  • Charlap, Leonard S., Bieberbach Groups and Flat Manifolds. Universitext. Springer-Verlag, New York, 1986. xiv+242 pp. ISBN: 0-387-96395-2 MR0862114 (88j:57042). See p. 6.
  • C. Cid, T. Schulz: Computation of Five and Six Dimensional Bieberbach Groups, Experimental Mathematics 10:1 (2001), 109-115
  • Manuel Caroli, Monique Teillaud. Delaunay triangulations of closed Euclidean dorbifolds. Discrete and Computational Geometry, Springer Verlag, 2016, 55 (4), pp.827-853. 10.1007/s00454-016-9782-6, hal-01294409; https://hal.inria.fr/hal-01294409/document

Links

  • W. Plesken and T. Schulz, The CARAT Homepage
  • W. Plesken and T. Schulz, CARAT Homepage [Cached copy in pdf format (without subsidiary pages), with permission]
  • W. Plesken and T. Schulz, Introduction to CARAT [Cached copy in pdf format (without subsidiary pages), with permission]

Crossrefs

Cf. A004027, A004028, A004029, A059105.

A059105 Number of n-dimensional torsion-free crystallographic groups with trivial center.

Original entry on oeis.org

0, 0, 1, 4, 101, 5004
Offset: 1

Views

Author

Tilman Schulz (tilman(AT)momo.math.rwth-aachen.de), Feb 13 2001

Keywords

Links

  • W. Plesken and T. Schulz, CARAT Homepage
  • W. Plesken and T. Schulz, CARAT Homepage [Cached copy in pdf format (without subsidiary pages), with permission]
  • W. Plesken and T. Schulz, Introduction to CARAT [Cached copy in pdf format (without subsidiary pages), with permission]

Crossrefs

Cf. A004027, A004028, A004029, A059104.

A307288 Number of arithmetic classes of space groups in dimension n, including enantiomorphs.

Original entry on oeis.org

1, 2, 13, 73, 780, 6079
Offset: 0

Views

Author

N. J. A. Sloane, Apr 08 2019

Keywords

Links

  • R. L. E. Schwarzenberger, Colour symmetry, Bulletin of the London Mathematical Society 16.3 (1984): 216-229.
  • Wikipedia, Space group

Crossrefs

For the case when enantiomorphs are not included see A004027.

A052487 Number of maximal irreducible integral matrix groups in n dimensions.

Original entry on oeis.org

1, 2, 3, 6, 7, 17, 7, 26, 20, 46, 9
Offset: 1

Views

Author

Frederick G. Schmitt (fred(AT)marin.cc.ca.us), Mar 16 2000

Keywords

References

  • Peter Engel, Geometric Crystallography, D. Reidel, Dordrecht, Holland, 1986. ISBN 90-277-2339-7. See Table 6.3, p. 111.

Links

Crossrefs

Cf. A004027.

Extensions

a(10) from Souvignier and a(11) from Conway & Sloane added by Andrey Zabolotskiy, Apr 17 2023
Showing 1-10 of 10 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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