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Moments of inertia associated with the lozenge tilings of a hexagon. (English) Zbl 0968.05018

Summary: Consider the probability that an arbitrary chosen lozenge tiling of the hexagon with side lengths \(a, b, c, a, b, c\) contains the horizontal lozenge with lowest vertex \((x,y)\) as if it described the distribution of mass in the plane. We compute the horizontal and the vertical moments of inertia with respect to this distribution. This solves a problem by Propp.

MSC:

05B45 Combinatorial aspects of tessellation and tiling problems
52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)
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