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An exact result for \((0, \pm \, 1)\)-vectors

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Abstract

After reviewing some memories and results of a dear friend and great collaborator, Michel-Marie Deza, a result (Theorem 8) is proven that could have very well been a joint paper, should not he have departed under tragical circumstances. This new result determines the maximum possible size of a family of \((0, \pm \, 1)\)-vectors without three vectors adding up to the all-zero vector.

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References

  1. Borg, P.: Intersecting systems of signed sets. Electron. J. Combin. 14, research paper R41 (2007)

  2. Cameron, P.J., Ku, C.Y.: Intersecting families of permutations. Eur. J. Combin. 24, 881–890 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Deza, M.: Solution d’un problème de Erdős–Lovász. J. Comb. Theory Ser. B 16, 166–167 (1974)

    Article  MATH  Google Scholar 

  4. Deza, M., Frankl, P.: On the maximum number of permutations with given maximal or minimal distance. J. Comb. Theory Ser. A 22, 352–360 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  5. Deza, M., Frankl, P.: Every large set of equidistant \((0, +1, -1)\)-vectors forms a sunflower. Combinatorica 1, 225–231 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ellis, D., Friedgut, E., Pilpel, H.: Intersecting families of permutations. J. Am. Math. Soc. 24, 649–682 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Erdős, P., Ko, C., Rado, R.: Intersection theorems for systems of finite sets. Q. J. Math. Oxf. 2(12), 313–320 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  8. Frankl, P.: The Erdős–Ko–Rado theorem is true for \(n=ckt\). Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. I, pp. 365–375, Colloq. Math. Soc. János Bolyai, 18, North-Holland, Amsterdam–New York (1978)

  9. Frankl, P., Füredi, Z.: The Erdős–Ko–Rado theorem for integer sequences. SIAM J. Algebraic Discrete Methods 1, 376–381 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kupavskii, A.: Explicit and probabilistic constructions of distance graphs with small clique numbers and large chromatic numbers. Izvest. Math. 78(N1), 59–89 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ponomarenko, E.I., Raigorodskii, A.M.: New upper bounds for the independence numbers with vertices at \({(1, 0, 1)}^n\) and their applications to the problems on the chromatic numbers of distance graphs. Mat. Zametki 96(N1), 138–147 (2014); English transl. Math. Notes 96(N1), 140–148 (2014)

  12. Raigorodskii, A.M.: Borsuk’s problem and the chromatic numbers of some metric spaces. Russ. Math. Surv. 56(N1), 103–139 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Wilson, R.M.: The exact bound in the Erdős–Ko–Rado theorem. Combinatorica 4, 247–257 (1984)

    Article  MathSciNet  MATH  Google Scholar 

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  1. Rényi Institute, Budapest, Hungary

    Peter Frankl

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  1. Peter Frankl
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Correspondence to Peter Frankl.

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Frankl, P. An exact result for \((0, \pm \, 1)\)-vectors. Optim Lett 12, 1011–1017 (2018). https://doi.org/10.1007/s11590-018-1245-y

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  • DOI: https://doi.org/10.1007/s11590-018-1245-y

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