On computing the total displacement number via weighted Motzkin paths
Data Structures and Algorithms
2020-08-27 v1 Discrete Mathematics
Combinatorics
Abstract
Counting the number of permutations of a given total displacement is equivalent to counting weighted Motzkin paths of a given area (Guay-Paquet and Petersen, 2014). The former combinatorial problem is still open. In this work, we show that this connection allows to construct efficient algorithms for counting and for sampling such permutations. These algorithms provide a tool to better understand the original combinatorial problem. A by-product of our approach is a different way of counting based on certain building sequences for Motzkin paths, which may be of independent interest.
Cite
@article{arxiv.1606.05538,
title = {On computing the total displacement number via weighted Motzkin paths},
author = {Andreas Bärtschi and Barbara Geissmann and Daniel Graf and Tomas Hruz and Paolo Penna and Thomas Tschager},
journal= {arXiv preprint arXiv:1606.05538},
year = {2020}
}
Comments
19 pages. An extended abstract of this paper will be published at the 27th International Workshop on Combinatorial Algorithms 2016, IWOCA'16