The Dimension of Divisibility Orders and Multiset Posets

被引：0
|
作者：
Haiman, Milan [1 ]
机构：
[1] MIT, Cambridge, MA 02139 USA
来源：
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2024年 / 41卷 / 03期
基金：
美国国家科学基金会;
关键词：
Partially ordered sets; Dimension; Multisets; Divisibility; SETS;
D O I：
10.1007/s11083-023-09653-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Dushnik-Miller dimension of a poset P is the least d for which P can be embedded into a product of d chains. Lewis and Souza isibility order on the interval of integers [N/kappa, N] is bounded above by kappa (log kappa)(1+o(1)) and below by Omega ((log kappa/log log kappa)(2)). We improve the upper bound to O((log kappa)(3)/(log log kappa)(2)). We deduce this bound from a more general result on posets of multisets ordered by inclusion. We also consider other divisibility orders and give a bound for polynomials ordered by divisibility.
引用
收藏
页码：693 / 707
页数：15
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