Explicit enumeration of triangulations with multiple boundaries
Maxim Krikun (IECN)
TL;DR
This paper presents a combinatorial approach to count rooted triangulations of a sphere with multiple holes based on edges and boundary lengths, utilizing Tutte's identity.
Contribution
It introduces an explicit enumeration method for complex triangulations with multiple boundaries, expanding combinatorial enumeration techniques.
Findings
Derived enumeration formulas for triangulations with multiple boundaries
Connected triangulation counts to Tutte's combinatorial identity
Enhanced understanding of boundary effects in spherical triangulations
Abstract
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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Topological and Geometric Data Analysis · Geometric and Algebraic Topology