Who knows of a way to describe the number of **weak exceedances of a permutation in terms of Dyck paths**?

Go to http://www.findstat.org/St000213, click on **search for statistic**, and you will find out that

- applying the inverse of the first fundamental transformation $\latex \phi$ given by sending the maximal entries in the cycles of a permutation to the left-to-right maxima of , then
- sending $\phi(\pi)$ to its increasing tree , and finally
- sending to the Dyck path by identifying an up step in with a left subtree in , and a down step inĀ with a right subtree in ,

will send the **number of weak exceedances** of to the **number of peaks of a Dyck path**.

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