Combinatorial theory and statistical design
This balanced and comprehensive treatment of topics in discrete mathematics and statistical design raises new questions and assesses potential difficulties surrounding various techniques. Covers a broad range of topics, from counting and enumeration techniques to graphs and networks, combinatorial and statistical designs, and partially ordered sets. Presents several methods of construction, many appearing for the first time in book form. Theory is carefully developed and presented in a conversational way that gears readers toward important new ideas and illustrates the necessity of introducing new techniques. Also examines the practical applications of results. Two entire sections are devoted to Polya's and DeBruign's enumeration of results, presenting them in the form of step-by-step recipes, ready for use by research workers.
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2-design Abelian group adjacency matrix association scheme automorphism group bijection blocks called cardinality classes coefficient color columns combinatorial complete graph compute conclude configurations contains count the number cube cycle index defined denote diagonal disjoint distinguished eigenvalues elements entries equals the number equation example exists factors finite follows formula geometry GF(q graph G group G Hadamard matrix Hence induced interactions isomorphic Kirchhoff matrix labeled lattice Laurent series lemma length linear main effects matroid maximal minimal Mobius function Mobius inversion modulo multiplication nonnegative nonsingular nonzero notation number of edges number of patterns Observe obtain optimal orbit orthogonal p-group pair parameters partially ordered set partitions path permutation points polynomial prove random variable reader result rotations satisfies Section sequence Show simple graph spanning trees square Statistical strongly regular graph subgroup of G subsets subspaces of dimension theorem theory total number vector space vertex vertices write zero