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

Autor: N N Kuzjurin, Konrad Engel
Rok vydání: 1985
Předmět:
Zdroj: Combinatorica. 5:301-309
ISSN: 1439-6912
0209-9683
DOI: 10.1007/bf02579244
Popis: 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.
Databáze: OpenAIRE
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