Geodesic
Moments of Inertia Associated with the Lozenge Tilings of a Hexagon
Séminaire lotharingien de combinatoire, Tome 45 (2000-2001) 
Ilse Fischer. Moments of Inertia Associated with the Lozenge Tilings of a Hexagon. Séminaire lotharingien de combinatoire, Tome 45 (2000-2001). http://geodesic.mathdoc.fr/item/SLC_2000-2001_45_a5/
@article{SLC_2000-2001_45_a5,
     author = {Ilse Fischer},
     title = {Moments of {Inertia} {Associated} with the {Lozenge} {Tilings} of a {Hexagon}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2000-2001},
     volume = {45},
     url = {http://geodesic.mathdoc.fr/item/SLC_2000-2001_45_a5/}
}
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%T Moments of Inertia Associated with the Lozenge Tilings of a Hexagon
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Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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).