On Computing the Total Displacement Number via Weighted Motzkin Paths
نویسندگان
چکیده
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 [10]). 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.
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