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Constructions of new q-cryptomorphisms
Journal of Combinatorial Theory Series B ( IF 1.4 ) Pub Date : 2021-12-17 , DOI: 10.1016/j.jctb.2021.12.001
Eimear Byrne , Michela Ceria , Relinde Jurrius

In the theory of classical matroids, there are several known equivalent axiomatic systems that define a matroid, which are described as matroid cryptomorphisms. A q-matroid is a q-analogue of a matroid where subspaces play the role of the subsets in the classical theory. In this article we establish cryptomorphisms of q-matroids. In doing so we highlight the difference between classical theory and its q-analogue. We introduce a comprehensive set of q-matroid axiom systems and show cryptomorphisms between them and existing axiom systems of a q-matroid. These axioms are described as the rank, closure, basis, independence, dependence, circuit, hyperplane, flat, open space, spanning space, non-spanning space, and bi-colouring axioms.



中文翻译:

新的 q-cryptomorphisms 的构造

在经典拟阵理论中,有几个已知的等价公理系统定义了拟阵,它们被描述为拟阵隐同态。一个q -matroid是q拟阵,其中子空间的经典理论发挥的子集的作用-analogue。在本文中,我们建立了q -拟阵的密码同态。在这样做时,我们强调了经典理论与其q模拟之间的区别。我们介绍了一套全面的q -拟阵公理系统,并展示了它们与q 的现有公理系统之间的密码态-拟阵。这些公理被描述为秩、闭包、基、独立、依赖、回路、超平面、平面、开放空间、跨越空间、非跨越空间和双色公理。

更新日期:2021-12-17
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