Titlebook: Asymptotic Combinatorics with Application to Mathematical Physics; Vadim Malyshev,Anatoly Vershik Book 2002 Kluwer Academic Publishers 200

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AVANT

Lecture Notes in Computer Sciencet show how to efficiently enumerate these diagrams (in time ~ 2.7.) by using a transfer matrix method. We give results for various generating functions up to 21 crossings. We then comment on their large-order asymptotic behavior.

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Hdl348

The Combinatorics of Alternating Tangles: From Theory to Computerized Enumerationt show how to efficiently enumerate these diagrams (in time ~ 2.7.) by using a transfer matrix method. We give results for various generating functions up to 21 crossings. We then comment on their large-order asymptotic behavior.

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Invariance Principles for Non-Uniform Random Mappings and Trees principle in two successive generalizations of the uniform case, to .-mappings (where elements are mapped to i.i.d. non-uniform elements) and .-mappings (where elements are mapped according to a Markov matrix). We compare with parallel results in the simpler setting of random trees.

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Zbigniew W. Raś,Maciek Michalewiczwe define two numbers .(.), .(.) . ℕ such that for any . obtained by natural operations from a representation . of dimension less than .(.) one has ..(.,..) = 0 for 0 < q < .(.). Applying this result to ..(.,.), we see that the vector bundle .., is rigid.

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Book 2002 of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.

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