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Combinatorial probabilities --- Probabilités combinatoires --- Probabilités combinatoires

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Combinatorial probabilities --- Random graphs --- Probabilités combinatoires --- Graphes aléatoires

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Combinatorial probabilities --- Probabilités combinatoires --- Statistique mathématique --- Mathematical statistics --- Analyse combinatoire --- Combinatorial probabilities. --- Mathematical statistics. --- Probabilités combinatoires --- Statistique mathématique --- Treillis, Théorie des

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Stochastic processes --- Discrete mathematics --- Combinatorial probabilities --- Probabilités combinatoires --- 519.212 --- Probabilistic combinatorics --- Probabilities --- Abstract probability theory. Combinatorial probabilities. Geometric probabilities --- Combinatorial probabilities. --- 519.212 Abstract probability theory. Combinatorial probabilities. Geometric probabilities --- Probabilités combinatoires

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This introduction to the recent theory of abstract tubes describes the framework for establishing improved inclusion-exclusion identities and Bonferroni inequalities, which are provably at least as sharp as their classical counterparts while involving fewer terms. All necessary definitions from graph theory, lattice theory and topology are provided. The role of closure and kernel operators is emphasized, and examples are provided throughout to demonstrate the applicability of this new theory. Applications are given to system and network reliability, reliability covering problems and chromatic graph theory. Topics also covered include Zeilberger's abstract lace expansion, matroid polynomials and Möbius functions.

Inequalities (Mathematics) --- Distribution (Probability theory) --- Combinatorial analysis. --- Combinatorial probabilities. --- Combinatorial analysis --- Combinatorial probabilities --- Inégalités (Mathématiques) --- Distribution (Théorie des probabilités) --- Analyse combinatoire --- Probabilités combinatoires --- Combinatorics. --- Algebra. --- Ordered algebraic structures. --- Probabilities. --- Order, Lattices, Ordered Algebraic Structures. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra --- Mathematical analysis --- Combinatorics