Notes on planar semimodular lattices. IV. The size of a minimal congruence lattice representation with rectangular lattices

被引：0

作者：

Gratzer, G. ^{[1
]}

Knapp, E. ^{[2
]}

机构：

[1] Univ Manitoba, Dept Math, Winnipeg, MB MB R3T, Canada

[2] Univ Manitoba, Winnipeg, MB R3T 2N2, Canada

来源：

ACTA SCIENTIARUM MATHEMATICARUM | 2010年 / 76卷 / 1-2期

基金：

加拿大自然科学与工程研究理事会;

关键词：

semimodular lattice; planar; congruence; rectangular;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let D be a finite distributive lattice with n join-irreducible elements. In Part III, we proved that D can be represented as the congruence lattice of a special type of planar semimodular lattices of O(n(3)) elements, we called rectangular. In this paper, we show that this result is best possible. Let D be a finite distributive lattice whose order of join-irreducible elements is a balanced bipartite order on n elements. Then any rectangular lattice L whose congruence lattice is isomorphic to D has at least kn3 elements, for some constant k > 0.

引用

页码：3 / 26

页数：24

共 38 条

[1] Notes on planar semimodular lattices. IV. The size of a minimal congruence lattice representation with rectangular lattices
G. Grätzer
E. Knapp
Acta Scientiarum Mathematicarum, 2010, 76 (1-2): : 3 - 26
[2] Notes on planar semimodular lattices. III. Rectangular lattices
Gratzer, G.
Knapp, E.
ACTA SCIENTIARUM MATHEMATICARUM, 2009, 75 (1-2): : 29 - 48
[3] Notes on planar semimodular lattices. VIII. Congruence lattices of SPS lattices
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[4] Notes on planar semimodular lattices. VIII. Congruence lattices of SPS lattices
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[5] Notes on Planar Semimodular Lattices. VII. Resections of Planar Semimodular Lattices
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Order, 2013, 30 : 847 - 858
[6] Notes on Planar Semimodular Lattices. VII. Resections of Planar Semimodular Lattices
Czedli, Gabor
Graetzer, George
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2013, 30 (03): : 847 - 858
[7] Notes on planar semimodular lattices. VI. On the structure theorem of planar semimodular lattices
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ALGEBRA UNIVERSALIS, 2013, 69 (04) : 301 - 304
[8] Notes on planar semimodular lattices. VI. On the structure theorem of planar semimodular lattices
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Algebra universalis, 2013, 69 : 301 - 304
[9] Notes on planar semimodular lattices. V. Cover-preserving embeddings of finite semimodular lattices into simple semimodular lattices
Gratzer, G.
Wares, T.
ACTA SCIENTIARUM MATHEMATICARUM, 2010, 76 (1-2): : 27 - 33
[10] Notes on planar semimodular lattices. V. Cover-preserving embeddings of finite semimodular lattices into simple semimodular lattices
G. Grätzer
T. Wares
Acta Scientiarum Mathematicarum, 2010, 76 (1-2): : 27 - 33

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