Walks in the quarter plane: Kreweras' algebraic model
From MaRDI portal
Publication:558684
DOI10.1214/105051605000000052zbMath1064.05010arXivmath/0401067OpenAlexW2034324189MaRDI QIDQ558684
Publication date: 13 July 2005
Published in: The Annals of Applied Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0401067
Exact enumeration problems, generating functions (05A15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)
Related Items (48)
The kernel method tail asymptotics analytic approach for stationary probabilities of two-dimensional queueing systems ⋮ Combinatorics meets potential theory ⋮ Walks confined in a quadrant are not always D-finite ⋮ On the set of zero coefficients of a function satisfying a linear differential equation ⋮ Bijective counting of Kreweras walks and loopless triangulations ⋮ Two non-holonomic lattice walks in the quarter plane ⋮ Asymptotic lattice path enumeration using diagonals ⋮ Counting coloured planar maps ⋮ An elementary solution of Gessel's walks in the quadrant ⋮ Walks with small steps in the 4D-orthant ⋮ Non-D-finite excursions in the quarter plane ⋮ Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity ⋮ New steps in walks with small steps in the quarter plane: series expressions for the generating functions ⋮ Rare event asymptotics for a random walk in the quarter plane ⋮ Waiting times in classical priority queues via elementary lattice path counting ⋮ Combinatorics arising from lax colimits of posets ⋮ Rényi entropy of the totally asymmetric exclusion process ⋮ Counting walks in a quadrant: a unified approach via boundary value problems ⋮ Permutations sortable by two stacks in parallel and quarter plane walks ⋮ The quasi-holonomic ansatz and restricted lattice walks ⋮ Survival time of a heterogeneous random walk in a quadrant ⋮ Tail asymptotics for a generalized two-demand queueing model -- a kernel method ⋮ On 3-dimensional lattice walks confined to the positive octant ⋮ Families of prudent self-avoiding walks ⋮ Counting permutations with no long monotone subsequence via generating trees and the kernel method ⋮ Kernel method and linear recurrence system ⋮ Lattice path counting and the theory of queues ⋮ The complete generating function for Gessel walks is algebraic ⋮ Exact tail asymptotics in a priority queue -- characterizations of the preemptive model ⋮ Promotion of Kreweras words ⋮ Asymptotics of lattice walks via analytic combinatorics in several variables ⋮ Counting colored planar maps: algebraicity results ⋮ Hypergeometric expressions for generating functions of walks with small steps in the quarter plane ⋮ Counting walks with large steps in an orthant ⋮ Classifying lattice walks restricted to the quarter plane ⋮ Square lattice walks avoiding a quadrant ⋮ Kernel method and system of functional equations ⋮ Quarter-plane lattice paths with interacting boundaries: Kreweras and friends ⋮ Enumeration of bilaterally symmetric 3-noncrossing partitions ⋮ Promotion of Kreweras words ⋮ Exact solutions of lattice polymer models ⋮ A human proof of Gessel’s lattice path conjecture ⋮ Exact solution of some quarter plane walks with interacting boundaries ⋮ Higher Dimensional Lattice Walks: Connecting Combinatorial and Analytic Behavior ⋮ Quarter-plane lattice paths with interacting boundaries: the Kreweras and reverse Kreweras models ⋮ A solution to the tennis ball problem ⋮ Random walks in cones ⋮ Exact tail asymptotics for a three-dimensional Brownian-driven tandem queue with intermediate inputs
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The ballot problem with three candidates
- D-finite power series
- A probabilistic method for lattice path enumeration
- Analytic models and ambiguity of context-free languages
- The diagonal of a D-finite power series is D-finite
- Differentiably finite power series
- A structured computer system model
- Generating functions for generating trees
- Four classes of pattern-avoiding permutations under one roof: Generating trees with two labels
- Linear recurrences with constant coefficients: The multivariate case
- Basic analytic combinatorics of directed lattice paths
- An analytical method in the theory of two-dimensional positive random walks
- Walks on the slit plane
- Walks confined in a quadrant are not always D-finite
- Two Parallel Queues Created by Arrivals with Two Demands I
- Singularity Analysis of Generating Functions
- Two parallel processors with coupled inputs
- Two coupled processors: The reduction to a Riemann-Hilbert problem
- Counting Walks in the Quarter Plane
- Topics in the Constructive Theory of Countable Markov Chains
- Walks on the slit plane: Other approaches
This page was built for publication: Walks in the quarter plane: Kreweras' algebraic model