%0 Generic %1 citeulike:71453 %A Hivert, F. %A Novelli, J. %A Thibon, J. %D 2004 %K algebra binary search trees %T The Algebra of Binary Search Trees %U http://arxiv.org/abs/math.CO/0401089 %X 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.

@misc{citeulike:71453, abstract = {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.}, added-at = {2007-08-18T13:22:24.000+0200}, author = {Hivert, F. and Novelli, J. and Thibon, J.}, biburl = {https://www.bibsonomy.org/bibtex/26b71bd27edb4fe1cf484f1209ebe95a1/a_olympia}, citeulike-article-id = {71453}, description = {citeulike}, eprint = {math.CO/0401089}, interhash = {f4d1ca16d8597cfe462405799794681a}, intrahash = {6b71bd27edb4fe1cf484f1209ebe95a1}, keywords = {algebra binary search trees}, month = {January}, timestamp = {2007-08-18T13:22:57.000+0200}, title = {The Algebra of Binary Search Trees}, url = {http://arxiv.org/abs/math.CO/0401089}, year = 2004 }