Analytic Combinatorics in Several Variables

Robin Pemantle; Mark C. Wilson; Stephen Melczer

doi:10.1017/9781108874144

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This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Baryshnikov, Yuliy Melczer, Stephen and Pemantle, Robin 2024. Asymptotics of Multivariate Sequences IV: Generating Functions with Poles on a Hyperplane Arrangement. Annals of Combinatorics, Vol. 28, Issue. 1, p. 169.

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Baryshnikov, Yuliy Jin, Kaitian and Pemantle, Robin 2024. Coefficient Asymptotics of Algebraic Multivariable Generating Functions. La Matematica, Vol. 3, Issue. 1, p. 293.

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Clemente, Lorenzo 2025. The commutativity problem for effective varieties of formal series, and applications. p. 804.

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Rosell, Aurelio Carnero Janssen, Niels Maselli, Antonella Pereda, Ernesto Huertas-Company, Marc and Kitaura, Francisco-Shu 2025. Scale-dependent brain age with cosmological higher-order statistics from structural magnetic resonance imaging. NeuroImage, Vol. 321, Issue. , p. 121500.

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Goodenough, Kenneth Coopmans, Tim and Towsley, Don 2025. On noise in swap ASAP repeater chains: exact analytics, distributions and tight approximations. Quantum, Vol. 9, Issue. , p. 1744.

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Lenz, Andreas Melczer, Stephen Rashtchian, Cyrus and Siegel, Paul H. 2025. Multivariate Analytic Combinatorics for Cost Constrained Channels. IEEE Transactions on Information Theory, Vol. 71, Issue. 11, p. 8223.

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Khera, Jessica and Lundberg, Erik 2025. The Distribution of the Length of the Longest Path in Random Acyclic Orientations of a Complete Bipartite Graph. Annals of Combinatorics,

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Kroitor, Alexander and Melczer, Stephen 2025. Completing the Asymptotic Classification of Mostly Symmetric Short Step Walks in an Orthant. Annals of Combinatorics, Vol. 29, Issue. 2, p. 575.

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2nd edition
Robin Pemantle, University of Pennsylvania, Mark C. Wilson, University of Massachusetts, Amherst, Stephen Melczer, University of Waterloo, Ontario

Publisher:: Cambridge University Press
Online publication date:: February 2024
Print publication year:: 2024
Online ISBN:: 9781108874144
DOI:: https://doi.org/10.1017/9781108874144

Subjects:: Mathematics (general), Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computer Science, Discrete Mathematics Information Theory and Coding
Series:: Cambridge Studies in Advanced Mathematics (212)

US$89.99

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Discrete structures model a vast array of objects ranging from DNA sequences to internet networks. The theory of generating functions provides an algebraic framework for discrete structures to be enumerated using mathematical tools. This book is the result of 25 years of work developing analytic machinery to recover asymptotics of multivariate sequences from their generating functions, using multivariate methods that rely on a combination of analytic, algebraic, and topological tools. The resulting theory of analytic combinatorics in several variables is put to use in diverse applications from mathematics, combinatorics, computer science, and the natural sciences. This new edition is even more accessible to graduate students, with many more exercises, computational examples with Sage worksheets to illustrate the main results, updated background material, additional illustrations, and a new chapter providing a conceptual overview.

‘A definitive treatment of a challenging but very useful subject. There is a wide variety of situations calling for the estimation of the coefficients of a multivariate generating function. The authors have done a superb job of classifying and elucidating the myriad of available techniques for achieving this aim.’

Richard P. Stanley - University of Miami

‘This book is an invaluable resource that is certain to have dramatic impact on research and teaching in this rapidly developing area of mathematics. The first edition broke new ground; this edition prepares the field for others to harvest new knowledge with important applications in many scientific disciplines.’

Robert Sedgewick - Princeton University

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Analytic Combinatorics in Several Variables

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