超图内外多项式良定性的一个直接初等证明
A direct and elementary proof of the well-definedness of the interior and exterior polynomials of hypergraphs
摘要：
T. Kálmán（A version of Tutte's polynomial for hypergraphs，Adv. Math. 244（2013）823-873.）引入了内部多项式和外部多项式，它们是平面点上Tutte多项式$T(x,y)$的推广，$(1/x,1)$和$(1,1/y)$。这两个多项式被定义在一个固定的超边的顺序，并证明是独立的顺序使用多面体的技术。本文类似于Tutte的原证明，对超图的内外多项式的良定性给出了一个直接的初等证明。
英文摘要：
T. Kálmán (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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