Asymptotics of the number of lattice triangulations of rectangles of width 4 and 5

2024/12/22 by S. Yu. Orevkov, Orevkov, Stepan
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.2412.17065

openalex publication_date 2024/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f(m,n) be the number of primitive lattice triangulations of an m × n rectangle. We express the limits lim_n f(m,n)^1/n for m = 4 and m=5 in terms of certain systems of Fredholm integral equations on generating functions (the case m≤3 was treated in a previous paper). Solving these equations numerically, we compute approximate values of these limits with a rather high precision.

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