An enumeration of equilateral triangle dissections

Details An enumeration of equilateral triangle dissections An enumeration of equilateral triangle dissections

2009-10-27

arxiv.org/abs/0910.5199v2

Mathematics

Combinatorics

Final version sent to journal.

Scientific paper

We enumerate all dissections of an equilateral triangle into smaller equilateral triangles up to size 20, where each triangle has integer side lengths. A perfect dissection has no two triangles of the same side, counting up- and down-oriented triangles as different. We computationally prove W. T. Tutte's conjecture that the smallest perfect dissection has size 15 and we find all perfect dissections up to size 20.

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