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-次赋值拟阵，该类包含拟阵的指示函数，并在取子式、对偶以及网络诱导等运算下封闭。我们基于稀疏铺砌拟阵构造了一类非R-次的赋值拟阵族。赋值拟阵与数理经济学中的总替代估值有着内在联系。藉此，我们反驳了Ostrovsky和Paes Leme（《理论经济学》2015）提出的“基于拟阵的估值猜想”，该猜想声称每个总替代估值均可通过反复应用合并与禀赋运算从加权拟阵秩函数得到。我们的结果在洛伦兹多项式领域亦具有意义：它揭示了已知构造运算的局限性。