The lattice of permutations is bounded

被引：12

作者：

Caspard, N ^{[1
]}

机构：

[1] Univ Paris Sud, LRI, F-91405 Orsay, France

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2000年 / 10卷 / 04期

关键词：

arrows relations; A-table; bounded lattice; lexicographical order; permutation;

D O I：

10.1142/S0218196700000182

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of this paper is to show that the lattice S-n of permutations on a n-element set is bounded. This result strengthens the semi-distributive nature of the lattice S-n. To prove this property, we use a characterization of the class of bounded lattices in terms of arrows relations defined on the join-irreducible elements of a lattice or, more precisely, in terms of the A-table of a lattice.

引用

页码：481 / 489

页数：9

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