About the ratio of the size of a maximum antichain to the size of a maximum level in finite partially ordered sets期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

About the ratio of the size of a maximum antichain to the size of a maximum level in finite partially ordered sets

Authors:	Konrad Engel Nikolaj Nikolajevič Kuzjurin

Institution:	1. Sektion Mathematik. Wilhelm-Pieck-Universit?t, 2500, Rostock, German Democratic Republic

Abstract:	LetP be a finite partially ordered set. The lengthl(x) of an elementx ofP is defined by the maximal number of elements, which lie in a chain withx at the top, reduced by one. Letw(P) (d(P)) be the maximal number of elements ofP which have the same length (which form an antichain). Further let $p^n : = \underbrace {PX...XP}_{n - times}$ . The numbers $r_k : = \mathop {\max }\limits_{P:\|P\| = k} \frac{{d(P)}}{{w(P)}}$ and $s_k : = \mathop {\max }\limits_{P:\|P\| = k} \mathop {\lim }\limits_{n \to \infty } \frac{{d(P^n )}}{{w(P^n )}}$ as well as all partially ordered sets for which these maxima are attained are determined.

Keywords:	06 A 10 05 A 99
本文献已被 SpringerLink 等数据库收录！