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 $n+1$…

Let $n$ be a positive integer. Let $D\mathcal{P}^{(2)}_{n,2n}(NE,EN)$ be the set of Delannoy paths from $(0,0)$ to $(n,2n)$ consisting of north-steps $N=(0,1)$, east-steps…