TY - GEN

T1 - Suitable permutations, Binary covering Arrays, and Paley matrices

AU - Colbourn, Charles

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Directed block design

KW - Golomb ruler

KW - Hadamard matrix

KW - Paley matrix

KW - Suitable sets of permutations

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U2 - 10.1007/978-3-319-17729-8_3

DO - 10.1007/978-3-319-17729-8_3

M3 - Conference contribution

AN - SCOPUS:84945897861

SN - 9783319177281

T3 - Springer Proceedings in Mathematics and Statistics

SP - 29

EP - 42

BT - Algebraic Design Theory and Hadamard Matrices, ADTHM 2014

A2 - Colbourn, Charles J.

PB - Springer New York LLC

T2 - Workshop on Algebraic Design Theory and Hadamard Matrices, ADTHM 2014

Y2 - 8 July 2014 through 11 July 2014

ER -