Lozenge Tilings Of the Equilateral Triangle
Combinatorics
2020-07-28 v2
Abstract
We consider incomplete tilings of the equilateral triangle of edge length n that is subdivided into n^2 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.
Keywords
Cite
@article{arxiv.1909.06336,
title = {Lozenge Tilings Of the Equilateral Triangle},
author = {Richard J. Mathar},
journal= {arXiv preprint arXiv:1909.06336},
year = {2020}
}
Comments
Version 2 includes a derivation/proof of the formula for sets with 4 lozenges