ON THE AUTOMORPHISM CONJECTURE FOR PRODUCTS OF ORDERED SETS

被引：1

作者：

KUZJURIN, NN ^{[1
]}

机构：

[1] RUSSIAN ACAD SCI,INST CYBERNET,MOSCOW 117312,RUSSIA

来源：

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 1992年 / 9卷 / 03期

关键词：

POSET; ORDER-PRESERVING MAP; AUTOMORPHISM; ENUMERATION;

D O I：

10.1007/BF00383944

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

1. Rival and A. Rutkowski conjectured that the ratio of the number of automorphisms of an arbitrary poset to the number of order-preserving maps tends to zero as the size of the poset tends to infinity. We prove this hypothesis for direct products of arbitrary posets P = S1 x ... x S(n) under the condition that max(i) \S(i)\ = o(square-root n/log n).

引用

页码：205 / 208

页数：4