Whaley's Theorem for Finite Lattices

被引：0
|
作者：
Ralph Freese
Jennifer Hyndman
J. B. Nation
机构：
[1] University of Hawaii,Department of Mathematics
来源：
Order | 2003年 / 20卷 / 3期
关键词：
lattice; ordered set; sublattice; maximal sublattice;
D O I：
10.1023/B:ORDE.0000026464.36426.09
中图分类号：
学科分类号：
摘要：
Whaley's Theorem on the existence of large proper sublattices of infinite lattices is extended to ordered sets and finite lattices. As a corollary it is shown that every finite lattice L with |L|≥3 contains a proper sublattice S with |S|≥|L|1/3. It is also shown that that every finite modular lattice L with |L|≥3 contains a proper sublattice S with |S|≥|L|1/2, and every finite distributive lattice L with |L|≥4 contains a proper sublattice S with |S|≥3/4|L|.
引用
收藏
页码：223 / 228
页数：5
相关论文
共 50 条
  • [21] On lattices from combinatorial game theory modularity and a representation theorem: Finite case
    Carvalho, Alda
    dos Santos, Carlos Pereira
    Dias, Catia
    Coelho, Francisco
    Neto, Joao Pedro
    Nowakowski, Richard
    Vinagre, Sandra
    THEORETICAL COMPUTER SCIENCE, 2014, 527 : 37 - 49
  • [22] S-fuzzy Version of Stone's Theorem for Distributive Lattices
    Y.S.Pawar
    S.S.Khopade
    模糊系统与数学, 2011, (04) : 47 - 54
  • [23] Finite-time fluctuation theorem for oscillatory lattices driven by a temperature gradient
    Li, Jinhong
    He, Dahai
    PHYSICAL REVIEW E, 2021, 103 (06)
  • [24] Finite rings and Wilson's theorem
    Hirano, Yasuyuki
    Matsuoka, Manabu
    TURKISH JOURNAL OF MATHEMATICS, 2013, 37 (04) : 571 - 576
  • [25] Finite Analogs of Szemeredi's Theorem
    Raff, Paul
    Zeilberger, Doron
    GEMS IN EXPERIMENTAL MATHEMATICS, 2010, 517 : 313 - 319
  • [26] Wick's theorem at finite temperature
    Evans, TS
    Steer, DA
    NUCLEAR PHYSICS B, 1996, 474 (02) : 481 - 496
  • [27] Wick's theorem at finite temperature
    Nucl Phys Sect B, 2 (481):
  • [28] Sklar's theorem in finite settings
    Mayor, Gaspar
    Suner, Jaume
    Torrens, Joan
    IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2007, 15 (03) : 410 - 416
  • [29] ON A THEOREM OF REPRESENTATION OF LATTICES
    WANG, SP
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 23 (03) : 583 - +
  • [30] Finite lattices as relative congruence lattices of finite algebras
    Nurakunov, A. M.
    ALGEBRA UNIVERSALIS, 2007, 57 (02) : 207 - 214
12345