Séminaire Lotharingien de Combinatoire, B65e (2011), 10 pp.

António Guedes de Oliveira and Michel Las Vergnas

Parking Functions and Labeled Trees

Abstract. We define a bijection between the set of parking functions of size n and the set of rooted (labeled) forests with n vertices for which the number of "probes" of the function is the number of inversions of the tree. This definition is not recursive.

Received: September 30, 2010. Revised: July 7, 2011; September 27, 2011, October 27, 2011. Accepted: November 10, 2011. Final Version: November 30, 2011.

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