The article describes the structural and algorithmic relations between Cartesian trees and Lyndon Trees. This leads to a uniform presentation of the Lyndon table of a word corresponding to the Next Nearest Smaller table of a sequence of numbers. It shows how to efficiently compute runs, that is, maximal periodicities occurring in a word.
@article{arxiv.1712.08749,
title = {Cartesian trees and Lyndon trees},
author = {Maxime Crochemore and Luis M. S. Russo},
journal= {arXiv preprint arXiv:1712.08749},
year = {2017}
}