Convex expansion for finite distributive lattices with applications

Abstract

The concept of cutting is first explicitly introduced. By the concept, a convex expansion for finite distributive lattices is considered. Thus, a more general method for drawing the Hasse diagram is given, and the rank generating function of a finite distributive lattice is obtained. In addition, we have several enumerative properties on finite distributive lattices and verify the generalized Euler formula for polyhedrons.