2 problems

Delannoy–Catalan bijection conjecture. For every positive integer $n$, there exists a bijection between $E\mathcal{P}^{(1)}_{n,n}(NE,EN)$ and the set of Catalan paths of size $n+1$…

For $n\geq 1$, let $W_{B_n}$ be the reflection group of type $B_n$. A type $B$ Catalan path of length $n$ is a lattice path of $2n$ north and east steps from $(0,0)$ staying above…