Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4624731 | Advances in Applied Mathematics | 2014 | 31 Pages |
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 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Jean-Christophe Aval, Adrien Boussicault, Mathilde Bouvel, Matteo Silimbani,