A direct and elementary proof of the well-definedness of the interior and exterior polynomials of hypergraphs
Abstract
T. K\'alm\'an (A version of Tutte's polynomial for hypergraphs, Adv. Math. 244 (2013) 823-873.) introduced the interior and exterior polynomials which are generalizations of the Tutte polynomial T(x,y) on plane points (1/x,1) and (1,1/y) to hypergraphs. The two polynomials are defined under a fixed ordering of hyperedges, and are proved to be independent of the ordering using techniques of polytopes. In this paper, similar to the Tutte's original proof we provide a direct and elementary proof for the well-definedness of the interior and exterior polynomials of hypergraphs.
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