Semimatroids and their Tutte polynomials
Semimatroids and their Tutte polynomials
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半拟阵及其 Tutte 多项式
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
Federico Ardila
中科院分区：
文献类型：
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作者：
Federico Ardila
我们定义并研究 emph{semimatroids}，一类抽象仿射超平面排列的依赖属性的对象。我们证明几何半格正是半拟阵平面的偏序集。我们定义并研究半拟阵的 Tutte 多项式。我们证明了它是半拟阵的通用 Tutte-Grothendieck 不变量，并给出了其非负整数系数的组合解释。
We define and study emph{semimatroids}, a class of objects which abstracts the dependence properties of an affine hyperplane arrangement. We show that geometric semilattices are precisely the posets of flats of semimatroids. We define and investigate the Tutte polynomial of a semimatroid. We prove that it is the universal Tutte-Grothendieck invariant for semimatroids, and we give a combinatorial interpretation for its non-negative integer coefficients.