Suitable permutations, Binary covering Arrays, and Paley matrices

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


A set of permutations of length ν 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, ADTHM 2014
EditorsCharles J. Colbourn
PublisherSpringer New York LLC
Number of pages14
ISBN (Print)9783319177281
StatePublished - 2015
EventWorkshop on Algebraic Design Theory and Hadamard Matrices, ADTHM 2014 - Lethbridge, Canada
Duration: Jul 8 2014Jul 11 2014

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


OtherWorkshop on Algebraic Design Theory and Hadamard Matrices, ADTHM 2014


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

ASJC Scopus subject areas

  • Mathematics(all)


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