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Séminaire Lotharingien de Combinatoire, B45f (2001), 14 pp.

# Ilse Fischer

#
Moments of Inertia Associated with the Lozenge Tilings of a Hexagon

**Abstract.**
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 (Problem 7 in
math.CO/9904150).

Received: January 16, 2001; Accepted: March 12, 2001.

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