Note on the description of join-distributive lattices by permutations

被引：12

作者：

Adaricheva, Kira ^{[1
,2
]}

Czedli, Gabor ^{[3
]}

机构：

[1] Yeshiva Univ, Dept Math Sci, New York, NY 10016 USA

[2] Nazarbayev Univ, Sch Sci & Technol, Dept Math, Astana 010000, Kazakhstan

[3] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary

来源：

ALGEBRA UNIVERSALIS | 2014年 / 72卷 / 02期

关键词：

join-distributive lattice; semimodular lattice; diamond-free lattice; trajectory; permutation; antimatroid; convex geometry; SEMIMODULAR LATTICES; CONVEX GEOMETRIES; FINITE;

D O I：

10.1007/s00012-014-0295-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let L be a join-distributive lattice with length n and width(JiL) a parts per thousand currency sign k. There are two ways to describe L by k - 1 permutations acting on an n-element set: a combinatorial way given by P.H. Edelman and R. E. Jamison in 1985 and a recent lattice theoretical way of the second author. We prove that these two approaches are equivalent. Also, we characterize join-distributive lattices by trajectories.

引用

页码：155 / 162

页数：8

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