### Abstract

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 language | English (US) |
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Title of host publication | Springer Proceedings in Mathematics and Statistics |

Publisher | Springer New York LLC |

Pages | 29-42 |

Number of pages | 14 |

Volume | 133 |

ISBN (Print) | 9783319177281 |

DOIs | |

Publication status | Published - 2015 |

Event | Workshop on Algebraic Design Theory and Hadamard Matrices, ADTHM 2014 - Lethbridge, Canada Duration: Jul 8 2014 → Jul 11 2014 |

### Other

Other | Workshop on Algebraic Design Theory and Hadamard Matrices, ADTHM 2014 |
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Country | Canada |

City | Lethbridge |

Period | 7/8/14 → 7/11/14 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Springer Proceedings in Mathematics and Statistics*(Vol. 133, pp. 29-42). Springer New York LLC. https://doi.org/10.1007/978-3-319-17729-8_3