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Ordering Block Designs

Part of the book series: CMS Books in Mathematics ((CMSBM))

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Abstract

In this chapter we provide the basic background necessary for understanding subsequent chapters. We begin with an introduction to the graph theory, designs and design theory concepts used throughout this monograph. The second half of the chapter deals with more advanced concepts, including configurations, Gray codes and universal cycles (Ucycles). We survey a broad range of results in existence and construction of combinatorial Gray codes and Ucycles for permutations, partitions and k-subsets of n-sets. Proofs are included to illustrate techniques in this area, especially when they shed light on similar techniques used in proving results on ordering the blocks of designs.This chapter is recommended to the reader who wants to read subsequent chapters and feels they need a primer on the background topics: graph theory, design theory, and combinatorial orderings.

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  1. School of Mathematics & Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada

    Megan Dewar & Brett Stevens

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  1. Megan Dewar
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Dewar, M., Stevens, B. (2012). Background. In: Ordering Block Designs. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4325-4_2

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