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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