We characterize a rich class of valuated matroids, called R-minor valuated matroids that includes the indicator functions of matroids, and is closed under operations such as taking minors, duality, and induction by network. We exhibit a family of valuated matroids that are not R-minor based on sparse paving matroids. Valuated matroids are inherently related to gross substitute valuations in mathematical economics. By the same token we refute the Matroid Based Valuation Conjecture by Ostrovsky and Paes Leme (Theoretical Economics 2015) asserting that every gross substitute valuation arises from weighted matroid rank functions by repeated applications of merge and endowment operations. Our result also has implications in the context of Lorentzian polynomials: it reveals the limitations of known construction operations.

翻译：我们刻画了一类丰富的赋值拟阵，称为R-子式赋值拟阵，其包含拟阵的示性函数，并且在取子式、对偶性及网络归纳等运算下封闭。我们基于稀疏铺砌拟阵展示了一族非R-子式的赋值拟阵。赋值拟阵在数理经济学中与总替代估值存在本质关联。基于同一原理，我们反驳了Ostrovsky与Paes Leme（Theoretical Economics 2015）提出的拟阵基估值猜想——该猜想断言所有总替代估值均可通过重复应用合并与禀赋操作从加权拟阵秩函数导出。我们的结论在洛伦兹多项式背景下亦具启示意义：它揭示了已知构造运算的局限性。