We recover the Tutte polynomial of a matroid, up to change of coordinates, from an Ehrhart-style polynomial counting lattice points in the Minkowski sum of its base polytope and scalings of simplices. Our polynomial has coefficients of alternating sign with a combinatorial interpretation closely tied to the Dawson partition. Our definition extends in a straightforward way to polymatroids, and in this setting our polynomial has Kálmán's internal and external activity polynomials as its univariate specialisations.

中文翻译：

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通过格点计数的 Tutte 多项式

我们恢复拟阵的 Tutte 多项式，直至坐标变化，从 Ehrhart 式多项式计算其基本多面体的 Minkowski 和中的格点和单纯形的标度。我们的多项式具有交替符号系数，其组合解释与 Dawson 分区密切相关。我们的定义以直接的方式扩展到多拟阵，在这种情况下，我们的多项式将 Kálmán 的内部和外部活动多项式作为其单变量特化。