**Contemporary Mathematics**

Volume: 520;
2010;
240 pp;
Softcover

MSC: Primary 05; 60; 41; 82;

Print ISBN: 978-0-8218-4783-1

Product Code: CONM/520

List Price: $83.00

Individual Member Price: $66.40

**Electronic ISBN: 978-0-8218-8199-6
Product Code: CONM/520.E**

List Price: $83.00

Individual Member Price: $66.40

# Algorithmic Probability and Combinatorics

Share this page *Edited by *
*Manuel E. Lladser; Robert S. Maier; Marni Mishna; Andrew Rechnitzer*

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.

#### Table of Contents

# Table of Contents

## Algorithmic Probability and Combinatorics

- Contents v6 free
- Preface vii8 free
- Walks with small steps in the quarter plane 110 free
- Quantum random walk on the integer lattice: Examples and phenomena 4150
- A case study in bivariate singularity analysis 6170
- Asymptotic normality of statistics on permutation tableaux 8392
- Rotor walks and Markov chains 105114
- Approximate enumeration of self-avoiding walks 127137
- Fuchsian differential equations from modular arithmetic 153163
- Random pattern-avoiding permutations 173183
- Analytic combinatorics in d variables: An overview 195205
- Asymptotic expansions of oscillatory integrals with complex phase 221231

#### Readership

Graduate students and research mathematicians interested in computational aspects of probability, combinatorics, and enumeration.