The dimension of suborders of the Boolean lattice

G. R. Brightwell; Henry Kierstead; A. V. Kostochka; W. T. Trotter

doi:10.1007/BF01108597

The dimension of suborders of the Boolean lattice

G. R. Brightwell, Henry Kierstead, A. V. Kostochka, W. T. Trotter

Mathematical and Statistical Sciences, School of (SoMSS)

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

10 Scopus citations

Abstract

We consider the order dimension of suborders of the Boolean lattice B_n. In particular we show that the suborder consisting of the middle two levels of B_n dimension at most of 6 log₃n. More generally, we show that the suborder consisting of levels s and s+k of B_n has dimension O(k² log n).

Original language	English (US)
Pages (from-to)	127-134
Number of pages	8
Journal	Order
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/BF01108597
State	Published - Jun 1 1994

Keywords

Bollean lattice
Mathematics Subject Classifications (1991): 06A07, 05C35
Ordered set
dimension
suborder

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology
Computational Theory and Mathematics

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10.1007/BF01108597

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abstract = "We consider the order dimension of suborders of the Boolean lattice Bn. In particular we show that the suborder consisting of the middle two levels of Bn dimension at most of 6 log3n. More generally, we show that the suborder consisting of levels s and s+k of Bn has dimension O(k2 log n).",

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AU - Brightwell, G. R.

AU - Kierstead, Henry

AU - Kostochka, A. V.

AU - Trotter, W. T.

PY - 1994/6/1

Y1 - 1994/6/1

N2 - We consider the order dimension of suborders of the Boolean lattice Bn. In particular we show that the suborder consisting of the middle two levels of Bn dimension at most of 6 log3n. More generally, we show that the suborder consisting of levels s and s+k of Bn has dimension O(k2 log n).

AB - We consider the order dimension of suborders of the Boolean lattice Bn. In particular we show that the suborder consisting of the middle two levels of Bn dimension at most of 6 log3n. More generally, we show that the suborder consisting of levels s and s+k of Bn has dimension O(k2 log n).

KW - Bollean lattice

KW - Mathematics Subject Classifications (1991): 06A07, 05C35

KW - Ordered set

KW - dimension

KW - suborder

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JO - Order

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ER -

The dimension of suborders of the Boolean lattice

Abstract

Keywords

ASJC Scopus subject areas

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