Matching fields were introduced by Sturmfels and Zelevinsky to study certain Newton polytopes, and more recently have been shown to give rise to toric degenerations of various families of varieties. Whenever a matching field gives rise to a toric degeneration, the associated polytope of the toric variety coincides with the matching field polytope. We study combinatorial mutations, which are analogues of cluster mutations for polytopes, of matching field polytopes and show that the property of giving rise to a toric degeneration of the Grassmannians, is preserved by mutation. Moreover, the polytopes arising through mutations are Newton-Okounkov bodies for the Grassmannians with respect to certain full-rank valuations. We produce a large family of such polytopes, extending the family of so-called block diagonal matching fields.

Sturmfels和Zelevinsky引入了匹配领域来研究某些牛顿多表位，并且最近发现它会引起各种变种的复曲面退化。每当匹配场引起复曲面退化时，复曲面变体的相关多位点与匹配场多位点重合。我们研究了组合突变，它们是多表位簇突变，匹配场多表位的类似物，并表明通过突变保留了引起格拉斯曼虫的复曲面退化的特性。此外，就某些满额估值而言，由突变产生的多表位是格拉斯曼主义者的牛顿-奥孔科夫体。我们生产大量此类多表位，扩展了所谓的块对角线匹配场的范围。