OFFSET
0,2
COMMENTS
In the Krasko paper p. 18, Table 2, this sequence is designated "tautilde^(3)_(+)(g)" and has offset 1. - Michael De Vlieger, Oct 31 2021
a(n-1) is the number of extremal Riemann surfaces of genus n, in the sense of having extremal injectivity radius; see the paper of Girondo and González-Diez. - Harry Richman, Jun 07 2024
LINKS
Roland Bacher and Alina Vdovina, Counting 1-vertex triangulations of oriented surfaces, arXiv:math/0110025 [math.CO], 2001.
Roland Bacher and Alina Vdovina, Counting 1-vertex triangulations of oriented surfaces, Discrete Math. 246 (2002), 13-27.
E. Girondo and G. González-Diez, Genus two extremal surfaces: Extremal discs, isometries and Weierstrass points, Isr. J. Math., 132 (2002), 221-238.
Evgeniy Krasko, Igor Labutin, and Alexander Omelchenko, Enumeration of 3-regular one-face maps on orientable or non-orientable surface up to all symmetries, arXiv:1901.06591 [math.CO], 2019.
FORMULA
Bacher & Vdovina reference gives a formula. Another formula can be derived by use of characters of the symmetric groups.
EXAMPLE
The first term, 1, is associated to the usual construction of the torus: identify opposite sides of a square. The 1-vertex triangulation is obtained by subdividing the square into 2 triangles along a diagonal. Another point of view is to identify opposite sides of a hexagon (thus getting a torus). The 1-vertex triangulation is the dual of the boundary of the hexagon (which is a graph having 2 nodes and a triple edge between them) drawn on the torus.
KEYWORD
nonn
AUTHOR
Roland Bacher, Mar 23 2002
STATUS
approved