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A derivation of the Catalan numbers from a bijection between permutations and labeled trees

Bennet Vance
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Abstract

We present an algorithmic mapping from permutations of length dn to labeled n-node d-ary trees and back again. Given such a bijection, one can interpret each of the factorials in the formula for the Catalan numbers as a count of permutations.

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Bennet Vance. 2001-12-11. A derivation of the Catalan numbers from a bijection between permutations and labeled trees. https://arxiv.org/abs/math/0112107

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