A Remark on the Paper “Properties of Intersecting Families of Ordered Sets” by O. Einstein

Combinatorica volume 38, pages1279–1284(2018)Cite this article

Abstract

O. Einstein (2008) proved Bollobás-type theorems on intersecting families of ordered sets of finite sets and subspaces. Unfortunately, we report that the proof of a theorem on ordered sets of subspaces had a mistake. We prove two weaker variants.

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References

  1. [1]

    L. Babai and P. Frankl: Linear algebra methods in combinatorics, Department of Computer Science, The University of Chicago, September 1992.

    Google Scholar 

  2. [2]

    B. Bollobás: On generalized graphs, Acta Math. Acad. Sci. Hungar 16 (1965) 447–452.

    MathSciNet  Article  MATH  Google Scholar 

  3. [3]

    O. Einstein: Properties of intersecting families of ordered sets, Combinatorica 28 (2008), 37–44.

    MathSciNet  Article  MATH  Google Scholar 

  4. [4]

    P. Frankl: An extremal problem for two families of sets, European J. Combin. 3 (1982), 125–127.

    MathSciNet  Article  MATH  Google Scholar 

  5. [5]

    Z. Füredi: Geometrical solution of an intersection problem for two hypergraphs, European J. Combin. 5 (1984), 133–136.

    MathSciNet  Article  MATH  Google Scholar 

  6. [6]

    L. Lovász: Flats in matroids and geometric graphs, in: Combinatorial surveys (Proc. Sixth British Combinatorial Conf., Royal Holloway Coll., Egham, 1977), 45–86. Academic Press, London, 1977.

    Google Scholar 

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Affiliations

  1. Department of Mathematical Sciences, KAIST, Daejeon, South Korea

    Sang-Il Oum & Sounggun Wee

Authors
  1. Sang-Il Oum
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  2. Sounggun Wee
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Corresponding author

Correspondence to Sang-Il Oum.

Additional information

Supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2017R1A2B4005020).

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Oum, SI., Wee, S. A Remark on the Paper “Properties of Intersecting Families of Ordered Sets” by O. Einstein. Combinatorica 38, 1279–1284 (2018). https://doi.org/10.1007/s00493-018-3812-3

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Mathematics Subject Classification (2010)

  • 05D05