Boolean Dimension of a Boolean Lattice

被引：0
|
作者：
Brianski, Marcin [1 ]
Hodor, Jedrzej [1 ,2 ]
La, Hoang [1 ]
Micek, Piotr [1 ]
Michno, Katzper [1 ]
机构：
[1] Jagiellonian Univ, Theoret Comp Sci Dept, Krakow, Poland
[2] Jagiellonian Univ, Krakow, Poland
来源：
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2024年
关键词：
Poset; Dimension; Boolean dimension; Boolean lattice; ORDER DIMENSION;
D O I：
10.1007/s11083-024-09666-w
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For every integer n with n >= 6, we prove that the Boolean dimension of a poset consistingof all the subsets of {1,...,n} equipped with the inclusion relation is strictly less than n.
引用
收藏
页数：12
相关论文
共 50 条
  • [1] THE DIMENSION OF SUBORDERS OF THE BOOLEAN LATTICE
    BRIGHTWELL, GR
    KIERSTEAD, HA
    KOSTOCHKA, AV
    TROTTER, WT
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 1994, 11 (02): : 127 - 134
  • [2] The dimension of neighboring levels of the Boolean lattice
    Kostochka, AV
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 1998, 14 (03): : 267 - 268
  • [3] The dimension of two levels of the Boolean lattice
    Kierstead, HA
    DISCRETE MATHEMATICS, 1999, 201 (1-3) : 141 - 155
  • [4] THE DIMENSION OF INTERIOR LEVELS OF THE BOOLEAN LATTICE
    HURLBERT, GH
    KOSTOCHKA, AV
    TALYSHEVA, LA
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 1994, 11 (01): : 29 - 40
  • [5] The Dimension of Neighboring Levels of the Boolean Lattice
    Kostochka A.V.
    Order, 1997, 14 (3) : 267 - 268
  • [6] The dimension of interior levels of the Boolean lattice - II
    Kostochka, AV
    Talysheva, LA
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 1998, 15 (04): : 377 - 383
  • [7] THE ORDER DIMENSION OF 2 LEVELS OF THE BOOLEAN LATTICE
    FUREDI, Z
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 1994, 11 (01): : 15 - 28
  • [8] The Dimension of Interior Levels of the Boolean Lattice, II
    A. V. Kostochka
    L. A. Talysheva
    Order, 1998, 15 : 377 - 383
  • [9] Boolean Dimension, Components and Blocks
    Tamás Mészáros
    Piotr Micek
    William T. Trotter
    Order, 2020, 37 : 287 - 298
  • [10] On the Boolean dimension of spherical orders
    Brightwell, GR
    Franciosa, PG
    ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 1996, 13 (03): : 233 - 243
12345