Abstract
A triangle contact system S is a geometrical object on the plane consisting of finite number of triangular disks {s 1,...,s n } in a triangle Δ bounded by three segments A, B and C such that every vertex of each si coincides with an inner point of either A, B, C or a segment of some s j . An orthogonal plane partition P is a geometrical object on the plane consisting of a finite number of horizontal segments a 1,..., a p and vertical segments b 1,..., b q in a rectangle R bounded by four segments A, B, C and D with A horizontal such that every endpoint of each a i coincides with an inner point of either B, D or some b j and that every endpoint of each b i coincides with an inner point of either A, C or some a j . From S and P, we can construct a plane triangulation and a plane quadrangulation according to the adjacency of elements in S and P, respectively. In this paper, we give a survey for triangle contact systems, orthogonal plane partitions and their graphs constructed from them.
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Nakamoto, A. (2001). Triangle Contact Systems, Orthogonal Plane Partitions, and their Hit Graphs. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_25
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DOI: https://doi.org/10.1007/3-540-47738-1_25
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