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

2,1

Comments

This includes subgroups of the full automorphism group.

Breuer's book erroneously gives a(33) = 2843. (See errata.)

References

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

Links

Table of n, a(n) for n=2..48.

Thomas Breuer, Errata et Addenda for Characters and Automorphism Groups of Compact Riemann Surfaces.

Jen Paulhus, Branching data for curves up to genus 48.

Example

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.

Crossrefs

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

Sequence in context: A140681 A262423 A020178 * A141556 A147281 A130062

Adjacent sequences: A347369 A347370 A347371 * A347373 A347374 A347375

Keyword

nonn,hard

Author

Eric M. Schmidt, Aug 29 2021

Status

approved