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Designs, Codes and Cryptography

, Volume 14, Issue 1, pp 5–22 | Cite as

Perfect Mendelsohn Packing Designs with Block Size Five

  • F. E. Bennett
  • J. Yin
  • H. Zhang
  • R. J. R. Abel
Article

Abstract

A (v, k, 1) perfect Mendelsohn packing design (briefly (v, k, 1)-PMPD) is a pair (X, A) where X is a v-set (of points) and A is a collection of cyclically ordered k-subsets of X (called blocks) such that every ordered pair of points of X appears t-apart in at most one block of A for all t = 1, 2,..., k-1. If no other such packing has more blocks, the packing is said to be maximum and the number of blocks in a maximum packing is called the packing number, denoted by P(v, k, 1). The values of the function P(v, 5, 1) are determined here for all v ≥5 with a few possible exceptions. This result is established by means of a result on incomplete perfect Mendelsohn designs which is of interest in its own right.

perfect Mendelsohn packing designs incomplete perfect Mendelsohn designs transversal designs 

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • F. E. Bennett
    • 1
  • J. Yin
    • 2
  • H. Zhang
    • 3
  • R. J. R. Abel
    • 4
  1. 1.Department of MathematicsMount Saint Vincent UniversityHalifaxCanada
  2. 2.Department of MathematicsSuzhou UniversitySuzhouP. R. China
  3. 3.Department of Computer ScienceUniversity of IowaIowa CityUSA
  4. 4.School of MathematicsUniversity of New South Wales, Kensington, NSW 2033Australia

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