Lozenge Tilings Of the Equilateral Triangle

2019/09/13 by Richard J. Mathar, Mathar, Richard J.
Computer Science · Mathematics · #52C20 (Primary) 05B45 (Secondary) #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1909.06336

openalex publication_date 2019/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider incomplete tilings of the equilateral triangle of edge length n that is subdivided into n² regular equilateral smaller unit triangles. Pairs of the unit triangles that share a side may be converted into lozenges, leaving some subset of the unit triangles untouched. We count numerically these coverings by lozenges and unit triangles for edge lengths n <= 6: the total and the detailed refinement as a function of the number of lozenges.

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