Comparing Dushnik-Miller Dimension, Boolean Dimension and Local Dimension
Comparing Dushnik-Miller Dimension, Boolean Dimension and Local Dimension
复制标题
比较 Dushnik-Miller 维数、布尔维数和局部维数
DOI：
10.1007/s11083-019-09502-6
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发表时间：
2017
期刊：
影响因子：
0.4
通讯作者：
W. T. Trotter
中科院分区：
文献类型：
--
作者：
F. Barrera;Thomas Prag;Heather C. Smith;Libby Taylor;W. T. Trotter
偏序集维度的最初概念是由Dushnik和Miller提出的，并在文献中得到了广泛的研究。最近，人们对称为布尔维和局部维的两种维的变体有了相当大的兴趣。对于偏序集P，P的布尔维和P的局部维都由P的维自上界，并且可以相当少。我们的主要目标将是研究这三个参数之间的类比和对比。作为一个例子，已知偏序集的维度作为其高度和其覆盖图的树宽的函数而有界。偏序集的布尔维是关于它的覆盖图的树宽的有界的，与它的高度无关。我们证明了偏序集的局部维度不能以其覆盖图的树宽为界，而与高度无关。我们还证明了偏序集的局部维度关于其覆盖图的路宽是有界的。在我们的几个结果中，将应用Ramsey理论方法。
The original notion of dimension for posets is due to Dushnik and Miller and has been studied extensively in the literature. Quite recently, there has been considerable interest in two variations of dimension known as Boolean dimension and local dimension. For a poset P, the Boolean dimension of P and the local dimension of P are both bounded from above by the dimension of P and can be considerably less. Our primary goal will be to study analogies and contrasts among these three parameters. As one example, it is known that the dimension of a poset is bounded as a function of its height and the tree-width of its cover graph. The Boolean dimension of a poset is bounded in terms of the tree-width of its cover graph, independent of its height. We show that the local dimension of a poset cannot be bounded in terms of the tree-width of its cover graph, independent of height. We also prove that the local dimension of a poset is bounded in terms of the path-width of its cover graph. In several of our results, Ramsey theoretic methods will be applied.
布尔维度和树宽度
影响因子：
1.1
作者：
S. Felsner;T. Mészáros;P. Micek
通讯作者：
P. Micek
具有平面覆盖图的偏序集的维数
影响因子：
0.7
作者：
Stefan Felsner;William T. Trotter;Veit Wiechert
通讯作者：
Veit Wiechert
DOI：
10.1016/j.jctb.2019.02.003
发表时间：
2019
期刊：
J. Comb. Theory, Ser. B
影响因子：
--
作者：
F. Barrera-Cruz;S. Felsner;T. Mészáros;P. Micek;H. Smith;L. Taylor;W. T. Trotter
通讯作者：
W. T. Trotter