作为希格斯提升序列子系统的Delta-拟阵
Delta-matroids as subsystems of sequences of Higgs lifts
AI总结：
本文围绕由希格斯提升序列得到的全希格斯提升Delta-拟阵，给出其及两类相关子式闭类的排除子式刻画，并刻画了可通过移除可行集得到Delta-拟阵的集系结构。
摘要：
在Tardos的论文《广义拟阵与超模着色》中，她研究了由希格斯提升序列得到的特殊Delta-拟阵；这些正是我们所要处理的全希格斯提升Delta-拟阵，我们所有的结果都围绕它们展开。我们在所有Delta-拟阵的范围内给出了全希格斯提升Delta-拟阵类的排除子式刻画，并且对我们利用希格斯提升定义的另外两个子式闭的Delta-拟阵类给出了类似的刻画。我们引入了一个由格路径产生的子式闭、对偶闭的希格斯提升Delta-拟阵类。由Bouchet的结果可知，所有Delta-拟阵都可以通过从全希格斯提升Delta-拟阵中移除某些可行集而得到；为了解决哪些可行集可以被移除的问题，我们在更一般的集系结构中给出了Delta-拟阵的排除子式刻画。当我们刻画那些可行集族是不同秩拟阵的基集族之并的Delta-拟阵时，这些排除子式中的许多会再次出现；而当我们要求这些拟阵具有特殊性质（例如为铺设拟阵）时，它们还会再次出现。
英文摘要：
In her paper "Generalized matroids and supermodular colourings", Tardos studied special delta-matroids obtained from sequences of Higgs lifts; these are the full Higgs lift delta-matroids that we treat and around which all of our results revolve. We give an excluded-minor characterization of the class of full Higgs lift delta-matroids within the class of all delta-matroids, and we give similar characterizations of two other minor-closed classes of delta-matroids that we define using Higgs lifts. We introduce a minor-closed, dual-closed class of Higgs lift delta-matroids that arise from lattice paths. It follows from results of Bouchet that all delta-matroids can be obtained from full Higgs lift delta-matroids by removing certain feasible sets; to address which feasible sets can be removed, we give an excluded-minor characterization of delta-matroids within the more general structure of set systems. Many of these excluded minors occur again when we characterize the delta-matroids in which the collection of feasible sets is the union of the collections of bases of matroids of different ranks, and yet again when we require those matroids to have special properties, such as being paving.
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