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Combinatorics of non-ambiguous trees.

Type of publication Peer-reviewed
Publikationsform Original article (peer-reviewed)
Author Jean-Christophe Aval, Adrien Boussicault, Mathilde Bouvel, Matteo Silimbani,
Project Permutation classes: from structure to combinatorial properties
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Original article (peer-reviewed)

Journal Advances in Applied Mathematics
Volume (Issue) 56
Page(s) 78 - 108
Title of proceedings Advances in Applied Mathematics

Open Access

Type of Open Access Repository (Green Open Access)


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 Steingrimsson. 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.