Skip to main content
SpringerLink
Log in

The dimension of suborders of the Boolean lattice

  • Published:
Order Aims and scope Submit manuscript

Abstract

We consider the order dimension of suborders of the Boolean latticeB n . In particular we show that the suborder consisting of the middle two levels ofB n dimension at most of 6 log3 n. More generally, we show that the suborder consisting of levelss ands+k ofB n has dimensionO(k 2 logn).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dushnik, B. (1950) Concerning a certain set of arrangements,Proc. Amer. Math. Soc. 1, 788–796.

    Google Scholar 

  2. Füredi, Z. personal communication.

  3. Füredi, Z., Hajnal, P., Rödl, V. and Trotter, W. T. (1991) Interval orders and shift graphs, in A. Hajnal and V. T. Sos (eds),Sets, Graphs and Numbers, Colloq. Math. Soc. Janos Bolyai60, 297–313.

    Google Scholar 

  4. Füredi, Z. and Kahn, J. (1986) On the dimensions of ordered sets of bounded degree,Order 3, 17–20.

    Google Scholar 

  5. Hurlbert, G., Kostochka, A. V. and Talysheva, L. A. On the dimension ofP(2,k;n) for largek, to appear.

  6. Spencer, J. (1972) Minimal scrambling sets of simple orders,Acta Math. Hungar. 22, 349–353.

    Google Scholar 

  7. Trotter, W. T. (1991)Combinatorics and Partially Ordered Sets: Dimension Theory, The Johns Hopkins University Press, Baltimore, Maryland.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, London School of Economics, Houghton Street, WC2A 2AE, London, UK

    G. R. Brightwell

  2. Department of Mathematics, Arizona State University, 85287, Tempe, Arizona, USA

    H. A. Kierstead & W. T. Trotter

  3. Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 630090, Novosibirsk 90, Russia

    A. V. Kostochka

  4. Bell Communications Research, 445 South Street 2L-367, 07962, Morristown, NJ, USA

    W. T. Trotter

Authors
  1. G. R. Brightwell
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. A. Kierstead
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. V. Kostochka
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. W. T. Trotter
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by W. T. Trotter

The research of the second author was supported by Office of Naval Research Grant N00014-90-J-1206.

The research of the third author was supported by Grant 93-011-1486 of the Russian Fundamental Research Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brightwell, G.R., Kierstead, H.A., Kostochka, A.V. et al. The dimension of suborders of the Boolean lattice. Order 11, 127–134 (1994). https://doi.org/10.1007/BF01108597

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01108597

Mathematics Subject Classifications (1991)

Key words

Search

Navigation