A347372 -id:A347372 - cp's OEIS frontend

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

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

Eric M. Schmidt, Aug 29 2021

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

Breuer's book erroneously gives a(33) = 949. (See errata.)

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

Thomas Breuer, Errata et Addenda for Characters and Automorphism Groups of Compact Riemann Surfaces.
Jen Paulhus, Branching data for curves up to genus 48.

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

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

Eric M. Schmidt, Aug 29 2021

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

Breuer's book erroneously gives a(33) = 576. (See errata.)

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

Thomas Breuer, Errata et Addenda for Characters and Automorphism Groups of Compact Riemann Surfaces.
Jen Paulhus, Branching data for curves up to genus 48.

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

Eric M. Schmidt, Aug 29 2021

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

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

Thomas Breuer, Errata et Addenda for Characters and Automorphism Groups of Compact Riemann Surfaces.
Jen Paulhus, Branching data for curves up to genus 48.

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

Eric M. Schmidt, Aug 29 2021

This includes subgroups of the full automorphism group.

Breuer's book erroneously gives a(33) = 1013. (See errata.)

			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]

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

Thomas Breuer, Errata et Addenda for Characters and Automorphism Groups of Compact Riemann Surfaces.
Jen Paulhus, Branching data for curves up to genus 48.

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

Eric M. Schmidt, Aug 29 2021

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

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

Thomas Breuer, Errata et Addenda for Characters and Automorphism Groups of Compact Riemann Surfaces.
Jen Paulhus, Branching data for curves up to genus 48.

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

cp's OEIS Frontend

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

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

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

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

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

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