Cyclic block designs from Skolem-type sequences

Silvesan, Daniela (2015) Cyclic block designs from Skolem-type sequences. Doctoral (PhD) thesis, Memorial University of Newfoundland.

[img] [English] PDF - Accepted Version
Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.

Download (613Kb)

Abstract

M. Colbourn and R. Mathon [45] asked: "Can Skolem's partitioning problems be generalized to yield cyclic BIBD(v; 4; 1)?". Rosa [76] asked: \What is the format of Skolem-type sequences that leads to cyclic BIBD(v; k; λ) for k [greater than or equal to] 4?". In this thesis, we will address these two questions. We introduce new Skolem-type sequences and then we use them to construct new cyclic BIBD(v; k; λ) for k [greater than or equal to] 3. Specifically, we use Skolem-type sequences to construct new cyclic BIBD(v; 3; λ) for all admissible orders v and λ. We use Skolem-type sequences to construct new cyclic BIBD(v; k; λ) for k [greater than or equal to] 4 and every v coprime with 6. We provide a complete set of examples of Skolem partitions that induce one cyclic BIBD(v; 4; λ) for every admissible class. We also use some known results and relative difference families to construct new cyclic BIBD(v; 4; λ) for infinite values of v. Moreover, we use Skolem-type sequences to construct cyclic, simple, and indecomposable BIBD(v; 3; 3) for every v with some possible exceptions for v = 9 and v = 24c + 9, c 4. We also construct infinitely many cyclically indecomposable but decomposable BIBD(v; 3; 4) for some orders v. Finally, we have many examples of simple and super-simple cyclic designs coming from Skolem-type sequences that produce optical orthogonal codes.

Item Type: Thesis (Doctoral (PhD))
URI: http://research.library.mun.ca/id/eprint/8406
Item ID: 8406
Additional Information: Includes bibliographical references (pages 178-189).
Keywords: cyclic designs
Department(s): Science, Faculty of > Mathematics and Statistics
Date: March 2015
Date Type: Submission
Library of Congress Subject Heading: Combinatorial designs and configurations; Sequences (Mathematics); Block designs

Actions (login required)

View Item View Item

Downloads

Downloads per month over the past year

View more statistics