Coxeter matroids generalize matroids just as flag varieties of Lie groups generalize Grassmannians. Valuations of Coxeter matroids are functions that behave well with respect to subdivisions of a Coxeter matroid into smaller ones. We compute the universal valuative invariant of Coxeter matroids. A key ingredient is the family of Coxeter Schubert matroids, which correspond to the Bruhat cells of flag varieties. In the process, we compute the universal valuation of generalized Coxeter permutohedra, a larger family of polyhedra that model Coxeter analogues of combinatorial objects such as matroids, clusters, and posets.

中文翻译：

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Coxeter拟阵的普遍估值

Coxeter拟阵推广拟​​阵，就像李群的标志变体推广Grassmannians一样。Coxeter拟阵的估值是在将 Coxeter拟阵细分为较小拟阵方面表现良好的函数。我们计算 Coxeter 拟阵的通用值不变量。一个关键成分是 Coxeter Schubert 拟阵家族，它对应于 flag 品种的 Bruhat 细胞。在这个过程中，我们计算了广义 Coxeter permutohedra 的通用估值，这是一个更大的多面体家族，它对拟阵、簇和偏集等组合对象的 Coxeter 类似物进行建模。