Can I read Block‐avoiding Point Sequencings on EtoBox?

Block‐avoiding Point Sequencings by Simon R. Blackburn; Tuvi Etzion is a Engineering article available to read on EtoBox.

What is Block‐avoiding Point Sequencings about?

Let n and l be positive integers. Recent papers by Kreher, Stinson, and Veitch have explored variants of the problem of ordering the points in a triple system (such as a Steiner triple system [STS], directed triple system, or Mendelsohn triple system) on n points so that no block occurs in a segment of l consecutive entries (thus the ordering is locally block-avoiding). We describe a greedy algorithm which shows that such an ordering exists, provided that n is sufficiently large when compared with l. This algorithm leads to im- proved bounds on the number of points in cases where this was known, but also extends the results to a significantly more general setting (which includes, e.g., orderings that avoid the blocks of a design). Similar results for a cyclic variant of this situation are also established. We construct STSs and quadruple systems where l can be large, showing that a bound of Stinson and Veitch is reasonable. Moreover, we generalize the Stinson-Veitch bound to a wider class of block designs and to the cyclic case. The results of Kreher, Stinson, and Veitch were originally inspired by results of Alspach, Kreher, and Pastine, who (motivated by zerosum avoiding sequence

Who reads Block‐avoiding Point Sequencings?

Author

Simon R. Blackburn; Tuvi Etzion

Publisher

Wiley

Published

2021

Language

EN

Field

Engineering (Physical Sciences)