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Two Bijections for Dyck Path Parameters

David Callan
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Abstract

Here we give two bijections, one to show that the number of UUU-free Dyck n-paths is the Motzkin number M_n, the other to obtain the (known) distributions of the parameters "number of UDUs" and "number of DDUs" on Dyck n-paths. The first bijection is straightforward, the second not quite so obvious.

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David Callan. 2004-07-20. Two Bijections for Dyck Path Parameters. https://arxiv.org/abs/math/0406381

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