The number of slim rectangular lattices

被引：4

作者：

Czedli, Gabor ^{[1
]}

Dekany, Tamas ^{[1
]}

Gyenizse, Gergo ^{[1
]}

Kulin, Julia ^{[1
]}

机构：

[1] Univ Szeged, Bolyai Inst, Aradi Vertanuk Tere 1, H-6720 Szeged, Hungary

来源：

ALGEBRA UNIVERSALIS | 2016年 / 75卷 / 01期

关键词：

rectangular lattice; patch lattice; semimodularity; slim lattice; planar lattice; combinatorics of permutations; SEMIMODULAR LATTICES; COMPOSITION SERIES; THEOREM;

D O I：

10.1007/s00012-015-0363-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Slim rectangular lattices are special planar semimodular lattices introduced by G. Gratzer and E. Knapp in 2009. They are finite semimodular lattices L such that the ordered set Ji L of join-irreducible elements of L is the cardinal sum of two nontrivial chains. After describing these lattices of a given length n by permutations, we determine their number, vertical bar SRectL(n)vertical bar. Besides giving recursive formulas, which are effective up to about n = 1000, we also prove that vertical bar SRectL(n)vertical bar is asymptotically (n - 2)! . e(2)/2. Similar results for patch lattices, which are special rectangular lattices introduced by G. Czedli and E. T. Schmidt in 2013, and for slim rectangular lattice diagrams are also given.

引用

页码：33 / 50

页数：18

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