Finite distributive lattices and the splitting property

被引：1
作者：
Duffus, D [1 ]
Sands, B
机构：
[1] Emory Univ, Dept Math & Comp Sci, Atlanta, GA 30322 USA
[2] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada
来源：
ALGEBRA UNIVERSALIS | 2003年 / 49卷 / 01期
关键词：
distributive lattice; maximal antichain; splitting property; splitting number; grid;
D O I：
10.1007/s000120300001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that a finite distributive lattice has the splitting property - every maximal antichain splits into two parts so that the lattice is the union of the upset of one part and the downset of the other - if and only if it is a Boolean lattice or is one of three other lattices. We also introduce a measure of "how splitting" a finite distributive lattice is, and investigate it.
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页码：13 / 33
页数：21
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