Abstract Given an assignment of real weights to the ground elements of a matroid, the min–max weight of a ground element e is the minimum, over all circuits containing e , of the maximum weight of an element in that circuit with the element e removed. We use this concept to answer the following structural questions for the minimum weight basis problem. Which elements are persistent under a given weighting (belong to all or to none of the optimal bases)? What changes of the weights are allowed while preserving optimality of optimal bases? How does the minimum weight of a basis change when the weight of a single ground element is changed, or when a ground element is contracted or deleted? Our answer to this latter question gives the tropical ( min , + , − ) analogue of Kirchhoff’s arithmetic ( + , × , ∕ ) effective conductance formula for electrical networks.

中文翻译：

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拟阵优化中的热带基尔霍夫公式和后最优性

摘要 给定拟​​阵的接地元素的实际权重分配，接地元素 e 的最小-最大权重是包含 e 的所有电路中该电路中删除元素 e 的元素的最大权重的最小值. 我们使用这个概念来回答以下最小权重基础问题的结构问题。哪些元素在给定的权重下是持久的（属于所有或不属于最佳基础）？在保持最优基的最优性的同时，允许权重发生哪些变化？当单个地元素的权重发生变化，或者当一个地元素被收缩或删除时，基础的最小权重如何变化？我们对后一个问题的回答给出了基尔霍夫算术 (+, ×,