The Algebra of Binary Search Trees
组合数学
2013-02-12 v2
摘要
We introduce a monoid structure on the set of binary search trees, by a process very similar to the construction of the plactic monoid, the Robinson-Schensted insertion being replaced by the binary search tree insertion. This leads to a new construction of the algebra of Planar Binary Trees of Loday-Ronco, defining it in the same way as Non-Commutative Symmetric Functions and Free Symmetric Functions. We briefly explain how the main known properties of the Loday-Ronco algebra can be described and proved with this combinatorial point of view, and then discuss it from a representation theoretical point of view, which in turns leads to new combinatorial properties of binary trees.
引用
@article{arxiv.math/0401089,
title = {The Algebra of Binary Search Trees},
author = {F. Hivert and J. -C. Novelli and J. -Y. Thibon},
journal= {arXiv preprint arXiv:math/0401089},
year = {2013}
}
备注
49 pages