Skip to main content
Springer Nature Link
Log in

Set systems with no union of cardinality 0 modulom

  • Original Papers
  • Published:
Save article
View saved research
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

Letq be a prime power. It is shown that for any hypergraphℱ = {F 1,...,F d(q−1)+1} whose maximal degree isd, there exists Ø ≠ ℱ0 ⊂ ℱ, such that

The alternative text for this image may have been generated using AI.

≡ 0 (modq).

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

Access this article

Log in via an institution

Subscribe and save

Springer+
from €37.37 /Month
  • Starting from 10 chapters or articles per month
  • Access and download chapters and articles from more than 300k books and 2,500 journals
  • Cancel anytime
View plans

Buy Now

Price includes VAT (Netherlands)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, books and news in related subjects, suggested using machine learning.

References

  1. Alon, N., Friedland, S. and Kalai, G.: Regular subgraphs of almost regular graphs. J. Comb. Theory, Ser. B.37, 79–91 (1984)

    Google Scholar 

  2. Baker, R.C., Schmidt, W.M.: Diophantine problems in variables restricted to the values 0 and 1. J. Number Theory12, 460–486 (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IBM Research Division K53/802, Almaden Research Center, 650 Harry Road, 95120-6099, San Jose, CA, USA

    N. Alon

  2. Math. Dept, 2-382-MIT, 02139, Cambridge, MA, USA

    D. Kleitman

  3. Princeton University, 08544, Princeton, NJ, USA

    R. Lipton

  4. Math. Dept., 2-382-MIT, 02139, Cambridge, MA, USA

    R. Meshulam

  5. Hebrew University and Harvard University, 02138, Cambridge, MA, USA

    M. Rabin

  6. Courant Institute, New York University, 251 Mercer Street, 10012, NY, USA

    J. Spencer

Authors
  1. N. Alon
    View author publications

    Search author on:PubMed Google Scholar

  2. D. Kleitman
    View author publications

    Search author on:PubMed Google Scholar

  3. R. Lipton
    View author publications

    Search author on:PubMed Google Scholar

  4. R. Meshulam
    View author publications

    Search author on:PubMed Google Scholar

  5. M. Rabin
    View author publications

    Search author on:PubMed Google Scholar

  6. J. Spencer
    View author publications

    Search author on:PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alon, N., Kleitman, D., Lipton, R. et al. Set systems with no union of cardinality 0 modulom . Graphs and Combinatorics 7, 97–99 (1991). https://doi.org/10.1007/BF01788135

Download citation

  • Received:

  • Revised:

  • Issue date:

  • DOI: https://doi.org/10.1007/BF01788135

Keywords