On a Surface Associated to the Catalan Triangle

Abstract

We define a surface that interpolates the ballot numbers in the Catalan triangle corresponding to every pair of nonnegative integers (except for the origin). We study the geometric properties of this surface and prove that it contains exactly five half-lines. The mean curvature and the Gauss curvature of the surface are also calculated.

Keywords

• Catalan numbers
• Catalan triangle
• immersions
• invariants
• Gauss curvature
• mean curvature