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

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

Author

Eric M. Schmidt, Aug 29 2021

Keywords

• nonn
• hard

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

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

Crossrefs

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