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.

A218877 Erroneous version of A179982.

Original entry on oeis.org

3, 7, 14, 17, 55, 73
Offset: 1

Views

Author

N. J. A. Sloane, Nov 25 2012

Keywords

Comments

Including in accordance with the OEIS policy of listing published but incorrect sequences, to serve as pointers towards the correct versions.

References

  • Sah, Chih-han, Groups related to compact Riemann surfaces, Acta Math. 123 (1969) 13-42.
  • E. B. Vinber and O. V. Shvartsman, Riemann surfaces, Journal of Mathematical Sciences, 14, #1 (1980), 985-1020. Riemann surfaces, Algebra, Topologiya, Geometriya, Vol. 16 (Russian), pp. 191-245, 247 (errata insert), VINITI , Moscow, 1978.

A346293 Maximum possible order of the automorphism group of a compact Riemann surface of genus n.

Original entry on oeis.org

48, 168, 120, 192, 150, 504, 336, 320, 432, 240, 120, 360, 1092, 504, 720, 1344, 168, 720, 228, 480, 1008, 192, 216, 720, 750, 624, 1296, 672, 264, 720, 372, 1536, 1320, 544, 672, 1728, 444, 912, 936, 960, 410, 1512, 516, 1320, 2160, 384, 408
Offset: 2

Views

Author

Jianing Song, Jul 13 2021

Keywords

Comments

By Hurwitz's automorphisms theorem, a(n) <= 84*(n-1). The values n such that a(n) = 84*(n-1) are listed in A179982.
Breuer's book erroneously gives a(33) = 768. (See errata.) - Eric M. Schmidt, Jul 29 2021

Examples

			The Bolza surface is a compact Riemann surface of genus 2 whose automorphism group is of the highest possible order (order 48, isomorphic to GL(2,3)), so a(2) = 48.

References

  • Thomas Breuer, Characters and automorphism groups of compact Riemann surfaces, Cambridge University Press, 2000.

Links

Crossrefs

Cf. A179982.

Extensions

a(12)-a(48) from Eric M. Schmidt, Jul 29 2021

A347368 Number of signatures of Fuchsian groups leading to automorphism groups of Riemann surfaces of genus n.

Original entry on oeis.org

20, 41, 56, 65, 75, 98, 92, 135, 168, 145, 167, 222, 183, 254, 283, 281, 277, 398, 337, 436, 441, 391, 499, 637, 542, 638, 731, 689, 736, 921, 805, 950, 1019, 1013, 1150, 1346, 1140, 1325, 1518, 1520, 1535, 1805, 1670, 1946, 2084, 1950, 2167
Offset: 2

Views

Author

Eric M. Schmidt, Aug 29 2021

Keywords

Comments

This includes signatures leading to subgroups of the full automorphism group.
Breuer's book erroneously gives a(33) = 949. (See errata.)

References

  • Thomas Breuer, Characters and automorphism groups of compact Riemann surfaces, Cambridge University Press, 2000, p. 91.

Links

Crossrefs

Cf. A179982, A346293, A347369, A347370, A347371, A347372, A347373.

Formula

a(n) = A347369(n) + A347370(n).

A347369 Number of signatures of Fuchsian groups of orbit genus 0 leading to automorphism groups of Riemann surfaces of genus n.

Original entry on oeis.org

18, 34, 47, 51, 63, 72, 74, 102, 130, 103, 128, 158, 136, 178, 200, 194, 197, 272, 235, 289, 299, 241, 337, 418, 354, 402, 477, 423, 471, 567, 503, 577, 618, 596, 704, 816, 672, 763, 903, 875, 891, 1028, 954, 1097, 1187, 1055, 1221
Offset: 2

Views

Author

Eric M. Schmidt, Aug 29 2021

Keywords

Comments

This includes signatures leading to subgroups of the full automorphism group.
Breuer's book erroneously gives a(33) = 576. (See errata.)

References

  • Thomas Breuer, Characters and automorphism groups of compact Riemann surfaces, Cambridge University Press, 2000, p. 91.

Links

Crossrefs

Cf. A179982, A346293, A347368, A347370, A347371, A347372, A347373.

A347370 Number of signatures of Fuchsian groups of positive orbit genus leading to automorphism groups of Riemann surfaces of genus n.

Original entry on oeis.org

2, 7, 9, 14, 12, 26, 18, 33, 38, 42, 39, 64, 47, 76, 83, 87, 80, 126, 102, 147, 142, 150, 162, 219, 188, 236, 254, 266, 265, 354, 302, 373, 401, 417, 446, 530, 468, 562, 615, 645, 644, 777, 716, 849, 897, 895, 946
Offset: 2

Views

Author

Eric M. Schmidt, Aug 29 2021

Keywords

Comments

This includes signatures leading to subgroups of the full automorphism group.

References

  • Thomas Breuer, Characters and automorphism groups of compact Riemann surfaces, Cambridge University Press, 2000, p. 91.

Links

Crossrefs

Cf. A179982, A346293, A347368, A347369, A347371, A347372, A347373.

A347371 Number of isomorphism types of automorphism groups of Riemann surfaces of genus n.

Original entry on oeis.org

19, 37, 44, 64, 59, 86, 65, 154, 119, 118, 98, 206, 99, 176, 139, 346, 117, 290, 136, 368, 187, 193, 171, 621, 184, 276, 306, 483, 187, 404, 189, 1014, 255, 332, 253, 880, 205, 381, 341, 1163, 244, 549, 244, 788, 436, 401, 273
Offset: 2

Views

Author

Eric M. Schmidt, Aug 29 2021

Keywords

Comments

This includes subgroups of the full automorphism group.
Breuer's book erroneously gives a(33) = 1013. (See errata.)

Examples

			The 19 automorphism groups for Riemann surfaces of genus 2 are the trivial group, C2, C3, C4, C2 X C2, C5, C6, S3, Q8, C8, D8, C10, C6 . C2, C2 X C6, D12, QD16, SL_2(3), (C2 X C6) . C2, and GL_2(3). [Breuer, Table 9 on p. 77]

References

  • Thomas Breuer, Characters and automorphism groups of compact Riemann surfaces, Cambridge University Press, 2000, p. 91.

Links

Crossrefs

Cf. A179982, A346293, A347368, A347369, A347370, A347372, A347373.

A347372 Number of signature-group pairs for Riemann surfaces of genus n.

Original entry on oeis.org

21, 49, 64, 93, 87, 148, 108, 268, 226, 232, 201, 453, 229, 408, 386, 733, 337, 791, 425, 941, 628, 718, 625, 1695, 715, 1101, 1147, 1642, 930, 1786, 1048, 2844, 1444, 1848, 1495, 3452, 1500, 2424, 2192, 4192, 2000, 3585, 2220, 4193, 3211, 3638, 2814
Offset: 2

Views

Author

Eric M. Schmidt, Aug 29 2021

Keywords

Comments

This includes subgroups of the full automorphism group.
Breuer's book erroneously gives a(33) = 2843. (See errata.)

Examples

			There are 20 signatures for genus 2. Of these, the signature (0; 2, 2, 3, 3) leads to both C6 and S3. Thus the total number of signature-group pairs is 21.

References

  • Thomas Breuer, Characters and automorphism groups of compact Riemann surfaces, Cambridge University Press, 2000, p. 91.

Links

Crossrefs

Cf. A179982, A346293, A347368, A347369, A347370, A347371, A347373.

A347373 Number of Aut(G)-orbits on G-characters that come from Riemann surfaces of genus n.

Original entry on oeis.org

21, 55, 73, 116, 105, 208, 141, 428, 335, 424, 329, 952, 365, 924, 789, 1834, 742, 2119, 936, 3365, 1762, 2694, 1812, 7274, 2058, 5109, 4024, 9812, 3706, 10258, 4404, 18905, 7664, 13482, 8041, 31541, 8473, 21882, 16148, 48952, 14259, 41110, 17308, 68873, 31616
Offset: 2

Views

Author

Eric M. Schmidt, Aug 29 2021

Keywords

Comments

Breuer's book erroneously gives a(33) = 18904. (See errata.)

References

  • Thomas Breuer, Characters and automorphism groups of compact Riemann surfaces, Cambridge University Press, 2000, p. 91.

Links

Crossrefs

Cf. A179982, A346293, A347368, A347369, A347370, A347371, A347372.

A343821 Numbers k such that the alternating group A_k is a Hurwitz group.

Original entry on oeis.org

15, 21, 22, 28, 29, 35, 36, 37, 42, 43, 45, 49, 50, 51, 52, 56, 57, 58, 63, 64, 65, 66, 70, 71, 72, 73, 77, 78, 79, 80, 81, 84, 85, 86, 87, 88, 91, 92, 93, 94, 96, 98, 99, 100, 101, 102, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122
Offset: 1

Views

Author

Eric M. Schmidt, Apr 30 2021

Keywords

Comments

This sequence contains every k > 167 [Conder].
This sequence is found in Section 2 of the Gordejuela and Martínez paper, which has a slight error: 86 occurs twice and 87 is missing.

Links

Crossrefs

Complement of A343822.
Cf. A179982.

A343822 Numbers k such that the alternating group A_k is not a Hurwitz group.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 38, 39, 40, 41, 44, 46, 47, 48, 53, 54, 55, 59, 60, 61, 62, 67, 68, 69, 74, 75, 76, 82, 83, 89, 90, 95, 97, 103, 104, 110, 111, 118, 125, 131, 139, 146, 167
Offset: 1

Views

Author

Eric M. Schmidt, Apr 30 2021

Keywords

Comments

Complement of A343821.
See the classification in section 5 of the first Conder reference. The term 139 is erroneously omitted there, as pointed out in the second Conder reference [Section 3].

Links

Crossrefs

Cf. A179982, A343821.
Showing 1-10 of 10 results.

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

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