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arXiv · 1305.3716

Combinatorics of non-ambiguous trees

Jean-Christophe Aval·Adrien Boussicault·Mathilde Bouvel·Matteo Silimbani
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Abstract

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 Steingr\'imsson. 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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Jean-Christophe Aval, Adrien Boussicault, Mathilde Bouvel, Matteo Silimbani. 2013-05-16. Combinatorics of non-ambiguous trees. https://arxiv.org/abs/1305.3716

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