The Dimension of Interior Levels of the Boolean Lattice, II

A. V. Kostochka; L. A. Talysheva

doi:10.1023/A:1006230818462

The Dimension of Interior Levels of the Boolean Lattice, II

Research output: Contribution to journal › Article › peer-review

Abstract

Extending an old lemma by Dushnik, we establish the dimension d(3, k; n) of the containment order generated by the 3-element and k-element subsets of an n-element set for most k between 2√n and n.

Original language	English (US)
Pages (from-to)	377-383
Number of pages	7
Journal	Order
Volume	15
Issue number	4
DOIs	https://doi.org/10.1023/A:1006230818462
State	Published - 1998
Externally published	Yes

Keywords

Boolean lattice
Dimension

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology
Computational Theory and Mathematics

Online availability

10.1023/A:1006230818462

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title = "The Dimension of Interior Levels of the Boolean Lattice, II",

abstract = "Extending an old lemma by Dushnik, we establish the dimension d(3, k; n) of the containment order generated by the 3-element and k-element subsets of an n-element set for most k between 2√n and n.",

keywords = "Boolean lattice, Dimension",

author = "Kostochka, {A. V.} and Talysheva, {L. A.}",

note = "Funding Information: ★★ This work was partially supported by the Network DIMANET of the European Union and the grant RPY300 of International Science Foundation and Russian Government. Funding Information: ★ This work was partially supported by the grant 96-01-01614 of the Russian Foundation for Fundamental Research and the grant RPY300 of International Science Foundation and Russian Government.",

year = "1998",

doi = "10.1023/A:1006230818462",

language = "English (US)",

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T1 - The Dimension of Interior Levels of the Boolean Lattice, II

AU - Kostochka, A. V.

AU - Talysheva, L. A.

N1 - Funding Information: ★★ This work was partially supported by the Network DIMANET of the European Union and the grant RPY300 of International Science Foundation and Russian Government. Funding Information: ★ This work was partially supported by the grant 96-01-01614 of the Russian Foundation for Fundamental Research and the grant RPY300 of International Science Foundation and Russian Government.

PY - 1998

Y1 - 1998

N2 - Extending an old lemma by Dushnik, we establish the dimension d(3, k; n) of the containment order generated by the 3-element and k-element subsets of an n-element set for most k between 2√n and n.

AB - Extending an old lemma by Dushnik, we establish the dimension d(3, k; n) of the containment order generated by the 3-element and k-element subsets of an n-element set for most k between 2√n and n.

KW - Boolean lattice

KW - Dimension

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The Dimension of Interior Levels of the Boolean Lattice, II

Abstract

Keywords

ASJC Scopus subject areas

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