2000 character limit reached
On computing the total displacement number via weighted Motzkin paths (1606.05538v1)
Published 17 Jun 2016 in cs.DS, cs.DM, and math.CO
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.