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A. Kasraoui and C. Krattenthaler

# Enumeration of symmetric centered rhombus tilings of a hexagon

**Abstract.** A rhombus tiling of a hexagon is said to be centered if it contains the central lozenge.
We compute the number of vertically symmetric rhombus tilings of a hexagon with side lengths $a, b, a, a, b, a$
which are centered. When $a$ is odd and $b$ is even, this shows that the probability that a random vertically
symmetric rhombus tiling of a $a, b, a, a, b, a$ hexagon is centered is exactly the same as the probability that a
random rhombus tiling of a $a, b, a, a, b, a$ hexagon is centered.
This also leads to a factorization theorem for the number of all rhombus tilings of a hexagon which are centered.

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