AI 中文总结
本文明确阐述魏对偶性与Fomin-Greene对偶性的关联，证明二者在魏数层面一致但在基础秩函数层面不一致，同时揭示偏序集的链与反链半拟阵无法通过标准半拟阵对偶复合关联。
AI 中文摘要
有限偏序集的Fomin-Greene对偶定理与半拟阵的魏对偶定理，均通过看似相似的对偶关系关联极值不变量集合，本文明确阐述二者的关联。研究表明，链数与反链数分别满足魏型对偶关系，对应反链删除数与链删除数；对任意至少含两个元素的偏序集，其链半拟阵与反链半拟阵无法通过标准半拟阵对偶操作的复合关联，但二者的上魏数可通过Fomin-Greene对偶相互确定，因此两种对偶关系在魏数层面一致，但在基础秩函数层面不一致。
英文摘要
The Fomin-Greene Duality Theorem for finite posets and Wei's Duality Theorem for demimatroids each relate sets of extremal invariants via seemingly similar dualities. This paper describes precisely how these two dualities relate. It is shown that the chain and antichain numbers each satisfy a Wei-type duality with antichain- and chain-deletion numbers, respectively, and that, for each poset with at least two elements, its chain and antichain demimatroids are not related by any composition of standard demimatroid duality operations. Their upper Wei-number numbers do however determine each other via Fomin-Greene duality. The two dualities thereby coincide for Wei numbers but not for the underlying rank functions.
