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luneburg h tools fundamental constructions combinatorial mathematics 1989

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Textbook in PDF format This definition of combinatorial mathematics to be found in Haider and Heise's book is certainly not the worst one. It implies in particular that combinatorics is not restricted to finite structures. But finiteness is always present and plays an essential role. Properties of finite sets are used permanently but usually unreflectedly: Proper subsets of a finite set have a smaller cardinal than the universe they belong to, injective mappings of a finite set into itself are surjective, and conversely. Moreover, finite sets admit essentially only one linear order. Finite topological spaces are always compact as their power set is finite. Foreword Hints for the reader Dedekind Triples: The Fundamental Gauge Finite Sets: The Basic Objects of Combinatorics Familiar Realizations of Dedekind Triples Adding without a Carry: Ein Glasperlenspiel Rudiments of Universal Algebra Embedding Commutative Semigroups into Groups: Localization The Revolving Door Algorithm Partitions of Finite Sets Gray Codes: The General Case A Little Bit on Graphs Operator Groups The Symmetric Groups: Combinatorial Properties The Symmetric Groups: Algebraic Properties Lyndon Words Galois Fields: Counting Irreducible Polynomials Ordered Sets The Axiom of Choice: Equivalent Principles and Consequences The Marriage Theorem Independence Structures Free Constructions Symmetric Polynomials Lie Algebras Ordered Groups The Fundamental Theorem of Algebra: A Final Highlight Bibliography Index of Algorithms and Procedures Index

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Luneburg H. Tools and Fundamental Constructions of Combinatorial Mathematics 1989.pdf 27.1 MB

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luneburg h tools fundamental constructions combinatorial mathematics 1989