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2007

Explicit enumeration of triangulations with multiple boundaries

Krikun, Maxim

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We enumerate rooted triangulations of a sphere with multiple holes by the total number of edges and the length of each boundary component.

The proof relies on a combinatorial identity due to W.T.
Tutte.

Explicit enumeration of triangulations with multiple boundaries · Around

Built on

A census of planar triangulations
W.T. Tutte · 1962
Earlier work this paper cites.
A census of slicings
W.T. Tutte · 1962
Earlier work this paper cites.
The enumeration of almost cubic maps
E. Nemeth R.C. Mullin and P.J. Schellenberg · 1970
Earlier work this paper cites.

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The asymptotic number of rooted maps on a surface
E.A. Bender and E.R. Canfield · 1986
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Quantum geometry: A Statistical Field Theory Approach
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The On-Line Encyclopedia of Integer Sequences
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Cited in the paper.

Then

Counting rooted maps on a surface
D. Arqués and A. Giorgetti · 2000
Later among the works it cites.
Boundaries of random triangulation of a disk
M. Krikun · 2003
Later among the works it cites.

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