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Enumeration of rhombus tilings of a hexagon which contain a fixed rhombus in the centre. (English) Zbl 1012.05011

This paper contains two new results in the enumeration of rhombus tilings: Translating tilings to determinants using the Gessel-Viennot “method” of nonintersecting lattice paths, the author obtains a triple sum, which then is evaluated by using hypergeometric transformations and summations. These computations yield the number of rhombus tilings of a hexagon with opposite sides of equal lengths, which contain the central rhombus, and the “next-to-central” rhombus, respectively.

MSC:

05A15 Exact enumeration problems, generating functions
05B45 Combinatorial aspects of tessellation and tiling problems
52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)

Software:

HYP
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References:

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