Some bijections for restricted Motzkin paths

Details Some bijections for restricted Motzkin paths Some bijections for restricted Motzkin paths

2004-07-22

arxiv.org/abs/math/0407374v1

Mathematics

Combinatorics

8 pages,LaTeX

Scientific paper

We give several bijections among restricted Motzkin paths, explaining why various parameters on these paths are equidistributed. For example, the number of doublerise-free Motzkin paths of length n is the same as the number of peak-free Motzkin paths of length n+1 and the parameter "number of doublefalls" has the same distribution on the former set as "number of valleys" does on the latter. The bijections are most easily presented recursively but we also give explicit descriptions using the notion of Motzkin tree.

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