Bressan 混合猜想、分支最优传输与组合优化之间的联系
Connections between Bressan's Mixing Conjecture, the Branched Optimal Transport and Combinatorial Optimization
AI总结：
本文研究 Bressan 混合猜想的一维形式，将其表述为经典最优传输、分支最优传输及组合优化问题，并证明离散情形下可行解数量与 Catalan 数量级相关。
摘要：
我们研究了著名的 Bressan 混合猜想的一维版本，并在经典最优传输设定、分支最优传输设定以及一种组合优化中引入了多种表述。在该组合问题的离散情形下，我们证明可行解的数量与 Catalan 数处于同一量级。我们的研究揭示了流体动力学中的混合问题与许多其他热门领域之间的复杂关系，并在跨学科的理论与实际应用中留下了许多有趣的开放问题。
英文摘要：
We investigate the 1D version of the notable Bressan's mixing conjecture, and introduce various formulation in the classical optimal transport setting, the branched optimal transport setting and a combinatorial optimization. In the discrete case of the combinatorial problem, we prove the number of admissible solutions is on the Catalan number. Our investigation sheds light on the intricate relationship between mixing problem in the fluid dynamics and many other popular fields, leaving many interesting open questions in both theoretical and practical applications across disciplines.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
