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
收藏
页码：481 / 489
页数：9
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