Drápal, Aleš; Hämäläinen, Carlo An enumeration of equilateral triangle dissections. (English) Zbl 1205.52014 Discrete Appl. Math. 158, No. 14, 1479-1495 (2010). A dissection of an equilateral triangle is a partition of the area in nonoverlapping equilateral triangles. The size of the dissection is the number of these nonoverlapping equilateral triangles. All triangles have integer side lengths. In a perfect dissection all triangles of the partition are different which means that they have different side lengths or different orientations (up- and down-oriented). In this paper the numbers of all dissections and all perfect dissections of an equilateral triangle up to size 20 are determined. It is proved in particular that Tutte’s conjecture that the smallest perfect dissection of an equilateral triangle has size 15 is true. Reviewer: Arnfried Kemnitz (Braunschweig) Cited in 1 Document MSC: 52C20 Tilings in \(2\) dimensions (aspects of discrete geometry) 52B45 Dissections and valuations (Hilbert’s third problem, etc.) 05A15 Exact enumeration problems, generating functions Keywords:triangle dissection; Latin trade; equilateral triangle; perfect dissection Software:plantri; SymPy PDFBibTeX XMLCite \textit{A. Drápal} and \textit{C. Hämäläinen}, Discrete Appl. Math. 158, No. 14, 1479--1495 (2010; Zbl 1205.52014) Full Text: DOI arXiv Online Encyclopedia of Integer Sequences: Number of isomorphism classes of separated dissections of an equilateral triangle into n nonoverlapping equilateral triangles. Number of perfect dissections of equilateral triangles into n equilateral triangles with integer sides. Size of largest triangle occurring in any of the possible dissections of an equilateral triangle into n equilateral triangles with integer sides, assuming gcd(s_1,s_2,...,s_n)=1, s_k being the side lengths. 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This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.