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.

引用

页码：13 / 33

页数：21

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