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Set systems with no union of cardinality 0 modulom

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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

≡ 0 (modq).

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References

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

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

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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
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  2. D. Kleitman
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  3. R. Lipton
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  4. R. Meshulam
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  5. M. Rabin
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  6. J. Spencer
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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

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

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