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Number of signature-group pairs for Riemann surfaces of genus n.
5

%I #8 Sep 14 2021 04:16:01

%S 21,49,64,93,87,148,108,268,226,232,201,453,229,408,386,733,337,791,

%T 425,941,628,718,625,1695,715,1101,1147,1642,930,1786,1048,2844,1444,

%U 1848,1495,3452,1500,2424,2192,4192,2000,3585,2220,4193,3211,3638,2814

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

%C This includes subgroups of the full automorphism group.

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

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

%H Thomas Breuer, <a href="http://www.math.rwth-aachen.de/~Thomas.Breuer/genus/doc/errata.pdf">Errata et Addenda for Characters and Automorphism Groups of Compact Riemann Surfaces</a>.

%H Jen Paulhus, <a href="https://paulhus.math.grinnell.edu/monodromy.html">Branching data for curves up to genus 48</a>.

%e 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.

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

%K nonn,hard

%O 2,1

%A _Eric M. Schmidt_, Aug 29 2021