We generalize the Tutte polynomial of a matroid to a morphism of matroids via the K-theory of flag varieties. We introduce two different generalizations, and demonstrate that each has its own merits, where the trade-off is between the ease of combinatorics and geometry. One generalization recovers the Las Vergnas Tutte polynomial of a morphism of matroids, which admits a corank-nullity formula and a deletion-contraction recursion. The other generalization does not, but better reflects the geometry of flag varieties.

中文翻译：

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拟态的K-理论Tutte多项式

我们通过标志变体的K-理论将拟阵的Tutte多项式推广为拟态的态。我们介绍了两种不同的概括，并证明了每种都有自己的优点，其中的折衷是在组合性和几何易用性之间进行权衡。一种概括是恢复拟阵拟态的Las Vergnas Tutte多项式，它接受零位粗略公式和删减收缩递归。另一种概括没有，但是更好地反映了标志变体的几何形状。