A priority queue transforms an input permutation p1 of a totally ordered set of size n into an output permutation p2. Atkinson and Thiyagarajah showed that the number of such pairs (p1; p2) is (n+1)n 1, which is well known to be the number of labeled trees on n + 1 vertices. We give a new proof of this result by finding a bijection from such pairs of permutations to labeled trees.

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