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A068182
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Number of combinatorially non-equivalent "triangulations" of a compact genus n surface which have only 1 vertex (all vertices of the triangles are identified). Also the number of combinatorially distinct identifications of pairs of edges of a polygone P having 12g-6 sides leading to a compact oriented genus g surface containing the boundary of P as a 3-regular graph.
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1, 9, 1726, 1349005, 2169056374, 5849686966988, 23808202021448662, 136415042681045401661, 1047212810636411989605202, 10378926166167927379808819918, 129040245485216017874985276329588
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| R. Bacher and A. Vdovina, Counting 1-vertex triangulations of oriented surfaces, Discrete Math. 246 (2002), 13-27.
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LINKS
| R. Bacher and A. Vdovina, Counting 1-vertex triangulations of oriented surfaces
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FORMULA
| Reference gives a formula. Another formula can be derived by use of characters of the symmetric groups.
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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.
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CROSSREFS
| Sequence in context: A197206 A197804 A047944 * A194135 A114224 A201845
Adjacent sequences: A068179 A068180 A068181 * A068183 A068184 A068185
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KEYWORD
| nonn
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AUTHOR
| Roland Bacher (Roland.Bacher(AT)ujf-grenoble.fr), Mar 23 2002
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