论文标题
星星和梳子II的双重定理II：主导星星和统治梳子
Duality theorems for stars and combs II: Dominating stars and dominated combs
论文作者
论文摘要
在一系列四篇论文中，我们确定了其存在是偶性的结构，从互补的意义上讲，对恒星或梳子的存在。在这里，在该系列的第二篇论文中，我们提出了二元定理，用于恒星和梳子的组合：主导恒星和主导的梳子。正如且仅在统治梳子时存在主导的恒星时，与它们的结构相吻合。像任意恒星和梳子一样，我们的二元定理（以及主导的恒星）用正常的树或树状分解来表达。 我们为主导的梳子提供的互补结构将恒星和梳子统一，并允许我们从二重性梳子中得出二元定理的二元定理。鉴于我们针对恒星和梳子的互补结构完全不同：恒星的互补结构是局部有限的，而这些结构是有限的，而梳子的梳子是无射线的。
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. Here, in the second paper of the series, we present duality theorems for combinations of stars and combs: dominating stars and dominated combs. As dominating stars exist if and only if dominated combs do, the structures complementary to them coincide. Like for arbitrary stars and combs, our duality theorems for dominated combs (and dominating stars) are phrased in terms of normal trees or tree-decompositions. The complementary structures we provide for dominated combs unify those for stars and combs and allow us to derive our duality theorems for stars and combs from those for dominated combs. This is surprising given that our complementary structures for stars and combs are quite different: those for stars are locally finite whereas those for combs are rayless.
