Partition-free families of sets

被引：7

作者：

Frankl, Peter ^{[1
]}

Kupayski, Andrey ^{[2
,3
]}

机构：

[1] Renyi Inst, Budapest, Hungary

[2] Moscow Inst Phys & Technol, Lab Adv Combinator & Networks Applicat, Moscow 141701, Moskovskaya Obl, Russia

[3] Univ Oxford, Math Inst, Oxford OX1 2JD, England

来源：

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2019年 / 119卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

05D05; 05D15 (primary); SUBSETS;

D O I：

10.1112/plms.12236

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let m(n) denote the maximum size of a family of subsets which does not contain two disjoint sets along with their union. In 1968, Kleitman proved that m(n)=nm+1+MIDLINE HORIZONTAL ELLIPSIS+n2m+1 if n=3m+1. Confirming the conjecture of Kleitman, we establish the same equality for the cases n=3m and n=3m+2, and also determine all extremal families. Unlike the case n=3m+1, the extremal families are not unique. This is a plausible reason behind the relative difficulty of our proofs. We completely settle the case of several families as well.

引用

页码：440 / 468

页数：29