The interior and exterior polynomials are well-defined

Interior and exterior polynomials, introduced by Kalman in Kalman, (2013), generalized the Tutte polynomial T(x, y) on plane points (1/x, 1) and (1, 1/y) from graphs to hypergraphs. Although the two polynomials were defined under a fixed ordering of hyperedges, they were proved to be independent of the orderings of hyperedges by using techniques of polytopes. Later, the two polynomials were unified to be the Tutte polynomial of polymatroids. The main purpose of this paper is to provide an alternative to Kalman's proof without using polytopes. Similar to the Tutte's original proof for the Tutte polynomial, our proof is direct and elementary.(c) 2023 Elsevier B.V. All rights reserved.