Algorithmic Probability and Combinatorics

Algorithmic Probability and Combinatorics

Pub. Date:
American Mathematical Society

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Algorithmic Probability and Combinatorics

This volume contains the proceedings of the AMS Special Sessions on Algorithmic Probability and Combinatorics held at DePaul University on October 5-6, 2007 and at the University of British Columbia on October 4-5, 2008. This volume collects cutting-edge research and expository on algorithmic probability and combinatorics. It includes contributions by well-established experts and younger researchers who use generating functions, algebraic and probabilistic methods as well as asymptotic analysis on a daily basis. Walks in the quarter-plane and random walks (quantum, rotor and self-avoiding), permutation tableaux, and random permutations are considered. In addition, articles in the volume present a variety of saddle-point and geometric methods for the asymptotic analysis of the coefficients of single- and multi-variable generating functions associated with combinatorial objects and discrete random structures. The volume should appeal to pure and applied mathematicians, as well as mathematical physicists; in particular, anyone interested in computational aspects of probability, combinatorics and enumeration. Furthermore, the expository or partly expository papers included in this volume should serve as an entry point to this literature not only to experts in other areas, but also to graduate students.

Product Details

ISBN-13: 9780821847831
Publisher: American Mathematical Society
Publication date: 07/30/2010
Series: Contemporary Mathematics Series , #520
Pages: 240
Product dimensions: 6.70(w) x 9.80(h) x 0.40(d)

Table of Contents


Walks with small steps in the quarter plane Marni Mishna Mishna, Marni 1

Quantum random walk on the integer lattice: Examples and phenomena Marko Petkovsek Petkovsek, Marko 41

A case study in bivariate singularity analysis Timothy Devries Devries, Timothy 61

Asymptotic normality of statistics on permutation tableaux Svante Janson Janson, Svante 83

Rotor walks and Markov chains James Propp Propp, James 105

Approximate enumeration of self-avoiding walks E. J. Janse van Rensburg van Rensburg, E. J. Janse 127

Fuchsian differential equations from modular arithmetic Iwan Jensen Jensen, Iwan 153

Random pattern-avoiding permutations Hailong Liu Liu, Hailong 173

Analytic combinatories in d variables: An overview Robin Pemantle Pemantle, Robin 195

Asymptotic expansions of oscillatory integrals with complex phase Mark C. Wilson Wilson, Mark C. 221

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