Propp conjectured that the number of lozenge tilings of a semiregular hexag
on of sides 2n - 1, 2n - 1, and 2n which contain the central unit rhombus i
s precisely one third of the total number of lozenge tilings. Motivated by
this, we consider the more general situation of a semiregular hexagon of si
des a, a, and b. We prove explicit formulas for the number of lozenge tilin
gs of these hexagons containing the central unit rhombus and obtain Propp's
conjecture as a corollary of our results. (C) 1999 Academic Press.