How many T-tessellations on $k$ lines? Existence of associated Gibbs measures on bounded convex domains

Jonas Kahn

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arXiv · 1012.2182

How many T-tessellations on $k$ lines? Existence of associated Gibbs measures on bounded convex domains

Jonas Kahn

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Abstract

The paper bounds the number of tessellations with T-shaped vertices on a fixed set of $k$ lines: tessellations are efficiently encoded, and algorithms retrieve them, proving injectivity. This yields existence of a completely random T-tessellation, as defined by Ki\^en Ki\^eu et al., and of its Gibbsian modifications. The combinatorial bound is sharp, but likely pessimistic in typical cases.

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Jonas Kahn. 2010-12-10. How many T-tessellations on $k$ lines? Existence of associated Gibbs measures on bounded convex domains. https://arxiv.org/abs/1012.2182

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