标题： 格值瓶颈对偶性 显示英文标题

标题： Lattice-Valued Bottleneck Duality

摘要： 此注释在序格的背景下重新表述了某些经典的组合对偶定理。 对于源-目标网络，我们将瓶颈路径-割和流-割对偶结果推广到分配格中的边容量。 对于偏序集，我们再次在分配格中推广了Dilworth定理的一个瓶颈版本。 这些结果适用于广泛的各种非数值网络流问题，如所示。 所有结果、证明和应用都是与AI语言模型合作完成的。 附录记录了它们的作用和影响。 显示英文摘要

摘要： This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capacities in a distributive lattice. For posets, we generalize a bottleneck version of Dilworth's theorem, again weighted in a distributive lattice. These results are applicable to a wide array of non-numerical network flow problems, as shown. All results, proofs, and applications were created in collaboration with AI language models. An appendix documents their role and impact.