Combinatorics of non-ambiguous trees
Combinatorics of non-ambiguous trees
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非歧义树的组合学
DOI：
10.1016/j.aam.2013.11.004
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
M. Silimbani
中科院分区：
文献类型：
--
作者：
J. Aval;A. Boussicault;M. Bouvel;M. Silimbani
本文研究了非二义树的组合性质。我们定义的这些对象可以被视为在带有一些约束的网格上绘制的二叉树，或者被视为先前由Aval、Boussicault和Nadeau定义的树状画面的子集。满足一些附加约束的非二义树的计数使我们能够给出Carlitz、Ehrenborg和Steingrímsson恒等式的巧妙的组合证明。我们还提供了一个钩子公式来计算具有给定基础树的非二义树的数目。最后，我们使用非二义树来描述平行四边形多项式和二叉树之间非常自然的双射。
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.