Construction of leaves and excesses when K=3,4

• Main Author: Zhong, Chao, 1979-
• Other Authors: Memorial University of Newfoundland. Dept. of Mathematics and Statistics
• Format: Thesis
• Language: English
• Published: 2007
• Subjects: Combinatorial packing and covering; Newfoundland studies; University of Newfoundland
• Online Access: http://collections.mun.ca/cdm/ref/collection/theses4/id/43723

Thesis (M.Sc.)--Memorial University of Newfoundland, 2008. Mathematics and Statistics Includes bibliographical references (leaves 89-94) A packing design , or a PD(v, k , λ) is a family of k -subsets (called blocks), of a v -set S , such that every 2-subset (called a pair ), of S is contained in at most λ blocks. The packing number P(v, k , λ) is the number of blocks in a PD(v, k , λ). -- The edges in the multigraph λKv not contained in the packing form the leave of the PD( v, k , λ), denoted by leave(v, k , λ). Generally we consider maximum packings (packings with maximum number of blocks) unless stated otherwise. -- A covering design , or a CD(v, k , λ) is a family of k -subsets (called blocks ), of a v -set S , such that every 2-subset (called a pair ), of S is contained in at least λ blocks. The covering number C(v, k , λ) is the number of blocks in a CD(v, k , λ). -- The extrone edges added to the multigraph λKv in the covering form the excess of the CD(v, k , λ), denoted by excess(v, k , λ). Generally we consider minimum coverings (coverings with minimum number of blocks) unless stated otherwise. -- In this thesis we give the direct constructions of the leaves and excesses for k = 3, 4. Some of them are from existing papers, some are the author's original work. This is the first time to put all the leaves and excesses for k = 4 and all λs together (with only few possible exceptions).