Five discordant permutations

  • Joseph M. Santmyer
Graphs and Combinatoric


A permutation π of1,2, …,π is5-discordant if π(i) ≠i, i + 1,i + 2, i + 3, i + 4 modn for 1 ≤in. A system of recurrences for computing the rook polynomials associated with5-discordant permutations is derived. This system, together with hit polynomials enable the5-discordant permutations to be enumerated.


Exclusion Principle Recurrence Formula Decomposition Tree Internal Vertex Fixed Cell 
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  1. 1.
    Bogart, K.: Introductory combinatorics, Marshfield: Pitman 1983MATHGoogle Scholar
  2. 2.
    Kaplansky, I., Riordan, J.: The problème des ménages. Scripta Math.12, 113–124 (1953)MathSciNetGoogle Scholar
  3. 3.
    Metropolis, N., Stein, M.L., Stein, P.R.: Permanents of cyclic (0,1) matrices. J. Com. Theory7, 291–304 (1969)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Riordan, J.: Discordant permutations. Scripta Math.20, 14–23 (1954)MATHMathSciNetGoogle Scholar
  5. 5.
    Riordan, J.: An introduction to combinatorial analysis. New Jersey: Princeton University Press 1978Google Scholar
  6. 6.
    Touchard, J.: Sur un probléme permutations. C. R. Acad. Sci. Paris.198, 631–633 (1934)Google Scholar
  7. 7.
    Whitehead, E.G., Jr.: “Four-discordant permutations”, J. Aust. Math. Soc. Ser.A 28, 369–377 (1979)MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Yamamoto, K.: Structure polynomial of latin rectangles and its application to a combinatorial problem. Mem. Fac. Sci. Kyrusyu Univ.10 Ser. A, 1–13 (1956)Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Joseph M. Santmyer
    • 1
  1. 1.Department of Mathematics and Computer ScienceCalifornia University of PennsylvaniaCaliforniaUSA

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