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Article Dans Une Revue Advances in Applied Mathematics Année : 2014

Combinatorics of non-ambiguous trees

Résumé

This article investigates combinatorial properties of non-ambiguous trees. These objects we define may be seen either as binary trees drawn on a grid with some constraints, or as a subset of the tree-like tableaux previously defined by Aval, Boussicault and Nadeau. The enumeration of non-ambiguous trees satisfying some additional constraints allows us to give elegant combinatorial proofs of identities due to Carlitz, and to Ehrenborg and Steingrímsson. We also provide a hook formula to count the number of non-ambiguous trees with a given underlying tree. Finally, we use non-ambiguous trees to describe a very natural bijection between parallelogram polyominoes and binary trees.
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hal-00988123 , version 1 (07-05-2014)

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Jean-Christophe Aval, Adrien Boussicault, Mathilde Bouvel, Matteo Silimbani. Combinatorics of non-ambiguous trees. Advances in Applied Mathematics, 2014, 56, pp.78-108. ⟨10.1016/j.aam.2013.11.004⟩. ⟨hal-00988123⟩

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