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How to get the Area of a Dyck path

Given a Dyck path $\pi$, $$\mathrm{Area}(\pi) = {(i,j)| i<j \text{="" and="" }="" (i,j)="" \text{="" under="" }="" \pi}.$$<="" p="">

How to get the area of a given Dyck path from some given DyckWord pi ?

How to get the Area of a Dyck path

Given a Dyck path $\pi$, $$\mathrm{Area}(\pi) = {(i,j)| i<j \text{="" the Area($\pi$) is the set of boxes $(i,j)$ such that $i<j$ and="" }="" (i,j)="" \text{="" $(i,j)$="" is="" under="" }="" \pi}.$$<="" $\pi$.<="" p="">

How to get the area of a given Dyck path from some given DyckWord pi ?

How to get the Area of a Dyck path

Given a Dyck path $\pi$, the Area($\pi$) is the set of boxes $(i,j)$ such that $i<j$ and="" $(i,j)$="" is="" under="" $\pi$.<="" p="">

How to get the area of a given Dyck path from some given DyckWord pi ?

How to get the Area of a Dyck path

Given a Dyck path $\pi$, the Area($\pi$) is the set of boxes $(i,j)$ such that $i<j$ and="" $(i,j)$="" is="" under="" $\pi$.<="" p=""> $i < j$ and $(i,j)$ is under $\pi$.

How to get the area of a given Dyck path from some given DyckWord pi ?