We study several consequences of the packing problem, a conjecture from combinatorial optimization, using algebraic invariants of square-free monomial ideals. While the packing problem is currently unresolved, we successfully settle the validity of its consequences. Our work prompts additional questions and conjectures, which are presented together with their motivation.

中文翻译：

---

包装问题的后果

我们使用无平方单项式理想的代数不变量，研究了组合优化的一个猜想，即包装问题的若干后果。尽管包装问题目前尚未解决，但我们成功解决了其后果的有效性。我们的工作提示了其他问题和猜想，并提出了它们的动机。