Four transformations on the Catalan triangle

الأصل · EN

In this paper, we define four transformations on the classical Catalan triangle C=(Cₙ,ₖ)ₙ≥ ₖ≥ ₀ with Cₙ,ₖ=k+1/n+12n-kn. The first three ones are based on the determinant and the forth is utilizing the permanent of a square matrix. It not only produces many known and new identities involving Catalan numbers, but also provides a new viewpoint on combinatorial triangles.