Counting finite lattices

被引：21
|
作者：
Heitzig, J [1 ]
Reinhold, J [1 ]
机构：
[1] Univ Hannover, Inst Math, D-30167 Hannover, Germany
来源：
ALGEBRA UNIVERSALIS | 2002年 / 48卷 / 01期
关键词：
orderly algorithm; (un-)labeled lattice; tree; canonical; levelized;
D O I：
10.1007/PL00013837
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The correct values for the number of all unlabeled lattices on n elements are known for n less than or equal to 11. We present a fast orderly algorithm generating all unlabeled lattices up to a given size n. Using this algorithm, we have computed the number of all unlabeled lattices as well as that of all labeled lattices on an n-element set for each n less than or equal to 18.
引用
收藏
页码：43 / 53
页数：11
相关论文
共 50 条
  • [1] Counting Finite Lattices
    Jobst Heitzig
    Jürgen Reinhold
    algebra universalis, 2002, 48 : 43 - 53
  • [2] Counting finite residuated lattices
    Belohlavek, Radim
    Vychodil, Vilem
    FOUNDATIONS OF FUZZY LOGIC AND SOFT COMPUTING, PROCEEDINGS, 2007, 4529 : 461 - +
  • [3] Counting weak Heyting algebras on finite distributive lattices
    Alizadeh, Majid
    Joharizadeh, Nima
    LOGIC JOURNAL OF THE IGPL, 2015, 23 (02) : 247 - 258
  • [4] COUNTING POINTS OF SCHEMES OVER FINITE RINGS AND COUNTING REPRESENTATIONS OF ARITHMETIC LATTICES
    Aizenbud, Avraham
    Avni, Nir
    DUKE MATHEMATICAL JOURNAL, 2018, 167 (14) : 2721 - 2743
  • [5] Embedding Finite Lattices into Finite Biatomic Lattices
    Kira Adaricheva
    Friedrich Wehrung
    Order, 2003, 20 : 31 - 48
  • [6] Embedding finite lattices into finite biatomic lattices
    Adaricheva, K
    Wehrung, F
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2003, 20 (01): : 31 - 48
  • [7] Counting arithmetic lattices and surfaces
    Belolipetsky, Mikhail
    Gelander, Tsachik
    Lubotzky, Alexander
    Shalev, Aner
    ANNALS OF MATHEMATICS, 2010, 172 (03) : 2197 - 2221
  • [8] Finite lattices as relative congruence lattices of finite algebras
    Nurakunov, A. M.
    ALGEBRA UNIVERSALIS, 2007, 57 (02) : 207 - 214
  • [9] COUNTING FORMULAS FOR GLUED LATTICES
    REUTER, K
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 1985, 1 (03): : 265 - 276
  • [10] Basic retracts and counting of lattices
    Bhavale, A. N.
    Waphare, B. N.
    AUSTRALASIAN JOURNAL OF COMBINATORICS, 2020, 78 : 73 - 99
12345