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Improved Bounds on Families Under k-wise Set-Intersection Constraints

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Abstract

Let p be a prime, and let L be a set of s congruence classes modulo p. Let \({\mathcal{H}}\) be a family of subsets of [n] such that the size modulo p of each member of \({\mathcal{H}}\) is not in L, but the size modulo p of every intersection of k distinct members of \({\mathcal{H}}\) is in L. We prove that \(|{{\mathcal{H}}}|\le(k-1)\sum_{i=0}^s {n-1\choose i}\) , improving the bound due to Grolmusz and generalizing results proved for k = 2 by Snevily.

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Authors and Affiliations

  1. Bloomberg Business Park, 100 Business Park Drive, Skillman, NJ, 08558-3629, U.S.A

    Weiting Cao

  2. General Eduation Dept., Kookmin University, 861-1 Jeongneung-dong Seongbuk-gu, Seoul, 136-702, Korea

    Kyung-Won Hwang

  3. Mathematics Dept., Univ. of Illinois, 1409 W. Green St., Urbana, IL, 61801, U.S.A

    Douglas B. West

Authors
  1. Weiting Cao
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  2. Kyung-Won Hwang
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  3. Douglas B. West
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Corresponding author

Correspondence to Douglas B. West.

Additional information

Work supported in part by the NSA under Award No. MDA904-03-1-0037.

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Cao, W., Hwang, KW. & West, D.B. Improved Bounds on Families Under k-wise Set-Intersection Constraints. Graphs and Combinatorics 23, 381–386 (2007). https://doi.org/10.1007/s00373-007-0741-0

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  • DOI: https://doi.org/10.1007/s00373-007-0741-0

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