发表机构
Amherst College; Davidson College（阿默斯特学院; 戴维森学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出一种极值集合论的解空间划分方法，结合可生成证明的MILP求解器，成功验证了Chvátal猜想的更大有限情形，效果优于look-ahead方法。
AI 中文摘要
我们提出一种用于划分极值集合论命题解空间的方法。与 look-ahead 这类与领域无关的划分方法相比，我们对候选解的构造策略进行案例分析。我们证明该方法能比 look-ahead 更有效地分解极值集合论问题。将此新划分策略与精确的可生成证明的 MILP 求解器结合，我们得以验证 Chvátal 猜想——这一极值组合学中悬而未决的长期问题——的更大有限情形，远超此前的工作。
英文摘要
We present a method for partitioning the solution space of statements in extremal set theory. Compared with domain-agnostic partitioning methods like look-ahead, we perform case analysis on the strategies by which a candidate solution can be constructed. We demonstrate that our approach can decompose problems in extremal set theory more effectively than look-ahead. Combining this new partitioning strategy with an exact proof-producing MILP solver, we are able to verify larger finite cases of Chvátal's Conjecture---a long-standing open question in extremal combinatorics---compared to previous work.
Comments14 pages; corrected the interchanged "max solve time (s)" values for "symbreak (1s)" and "symbreak (3s)" in Table II (p. 9)
DOI：10.34727/2026/isbn.978-3-85448-093-8_75
