Abstract
Interior and exterior polynomials, introduced by Kálmán in Kálmán, (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 Kálmán’s proof without using polytopes. Similar to the Tutte’s original proof for the Tutte polynomial, our proof is direct and elementary.
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