极值集合论问题的覆盖引理和q-类似物

IF 0.6 3区数学 Q3 MATHEMATICS

Ars Mathematica Contemporanea Pub Date : 2019-05-16 DOI:10.26493/1855-3974.2677.b7f

Dániel Gerbner

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引用次数: 1

摘要

我们证明了一个一般引理(灵感来自Holroyd和Talbot的一个引理)关于满足某种遗传性质的结构和满足相同遗传性质的子结构的最大基(或权)之间的联系。我们用它来说明布尔偏集中的禁止传票集问题的结果如何蕴涵有限向量空间的子空间的偏集中的类似结果。我们还研究了子空间的偏序集中的广义禁止传票集问题。

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The covering lemma and q-analogues of extremal set theory problems

We prove a general lemma (inspired by a lemma of Holroyd and Talbot) about the connection of the largest cardinalities (or weight) of structures satisfying some hereditary property and substructures satisfying the same hereditary property. We use it to show how results concerning forbidden subposet problems in the Boolean poset imply analogous results in the poset of subspaces of a finite vector space. We also study generalized forbidden subposet problems in the poset of subspaces.

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来源期刊

Ars Mathematica Contemporanea MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Ars mathematica contemporanea will publish high-quality articles in contemporary mathematics that arise from the discrete and concrete mathematics paradigm. It will favor themes that combine at least two different fields of mathematics. In particular, we welcome papers intersecting discrete mathematics with other branches of mathematics, such as algebra, geometry, topology, theoretical computer science, and combinatorics. The name of the journal was chosen carefully. Symmetry is certainly a theme that is quite welcome to the journal, as it is through symmetry that mathematics comes closest to art.