Subdivisions of integral base polytopes Original Research Article

A function defined on an integral base set induces a coherent polytopal subdivision of the integral base polytope. Such a coherent polytopal subdivision consists of integral base polytopes when the function is an M-convex function. We show such subdivisions form a filter with respect to refinement. We show that an integral base polytope can be divided into two integral base polytopes if and only if there exists a hyperplane by which the section of the polytope is an integral base polytope.