Largest Minimal Inversion-Complete and Pair-Complete Sets of Permutations

This is a preview of subscription content, access via your institution.

References

  1. [1]

    M. Bóna: Combinatorics of permutations, 2nd ed., CRC Press, Boca Raton, FL, 2012.

    Book  MATH  Google Scholar 

  2. [2]

    C. J. Colbourn: Suitable Permutations, Binary Covering Arrays and Paley Matrices, in: Algebraic Design Theory and Hadamard Matrices (C. J. Colbourn, ed.), Springer (2015), 29–42.

    Google Scholar 

  3. [3]

    B. Dushnik: Concerning a certain set of arrangements, Proc. Amer. Math. Soc. 1 (1950), 788–796.

    MathSciNet  Article  MATH  Google Scholar 

  4. [4]

    C. Malvenuto, P. Möseneder Frajria, L. Orsina and P. Papi: The maximum cardinality of minimal inversion complete sets in finite reflection groups, Journal of Algebra 424 (2015), 330–356.

    MathSciNet  Article  MATH  Google Scholar 

  5. [5]

    W. Mantel: Vraagstuk XXVIII, Wiskundige Opgaven met de Oplossingen 10 (1907), 60–61.

    MATH  Google Scholar 

  6. [6]

    B. H. Margolius: Permutations with inversions, Journal of Integer Sequences 4 (2001), Article 01.2.4(electronic).

  7. [7]

    G. Markowsky: Permutation lattices revisited, Mathematical Social Sciences 27 (1994), 59–72.

    MathSciNet  Article  MATH  Google Scholar 

  8. [8]

    K. Murota: Discrete convex analysis, SIAM Monographs on Discrete Mathematics and Applications 10, Philadelphia, 2003.

    Book  MATH  Google Scholar 

  9. [9]

    M. Queyranne and F. Tardella: Carathéodory, Helly and Radon Numbers for Sub- lattice Convexities in Euclidian, Integer and Boolean Spaces, Mathematics of Operation Research (in press) and CORE Discussion Paper 2015/10, Université catholique de Louvain, 2015.

    Google Scholar 

  10. [10]

    J. Spencer: Minimal scrambling sets of simple orders, Acta Math. Acad. Sci. Hung. 22 (1971/1972), 349–353.

    MathSciNet  Article  MATH  Google Scholar 

  11. [11]

    P. Turán: Egy gráfelméleti szélsőértékfeladatról, Mat. Fiz. Lapok 48 (1941), 436–453.

    MathSciNet  Google Scholar 

  12. [12]

    M. L. J. van de Vel: Theory of convex structures, North-Holland Mathematical Library, vol. 50, North-Holland Publishing Co., Amsterdam, 1993.

    MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Eric Balandraud.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Balandraud, E., Tardella, F. & Queyranne, M. Largest Minimal Inversion-Complete and Pair-Complete Sets of Permutations. Combinatorica 38, 29–41 (2018). https://doi.org/10.1007/s00493-016-3426-6

Download citation

Mathematics Subject Classification (2000)

  • 05D99
  • 05A05