Suitable permutations, binary covering arrays, and paley matrices

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Scopus citations


A set of permutations of length v is t-suitable if every element precedes every subset of t - 1 others in at least one permutation. The maximum length of a t-suitable set of N permutations depends heavily on the relation between t and N. Two classical results, due to Dushnik and Spencer, are revisited. Dushnik's result determines the maximum length when t > √2N. On the other hand, when t is fixed Spencer's uses a strong connection with binary covering arrays of strength t - 1 to obtain a lower bound on the length that is doubly exponential in t. We explore intermediate values for t, by first considering directed packings and related Golomb rulers, and then by examining binary covering arrayswhose number of rows is approximately equal to their number of columns. These in turn are constructed from Hadamard and Paley matrices, for which we present some computational data and questions.

Original languageEnglish (US)
Title of host publicationAlgebraic Design Theory and Hadamard Matrices
Subtitle of host publicationADTHM, Lethbridge, Alberta, Canada, July 2014
PublisherSpringer International Publishing
Number of pages14
ISBN (Electronic)9783319177298
ISBN (Print)9783319177281
StatePublished - Sep 3 2015


  • Directed block design
  • Golomb ruler
  • Hadamard matrix
  • Paley matrix
  • Suitable sets of permutations

ASJC Scopus subject areas

  • General Mathematics


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