A human proof of Gessel’s lattice path conjecture
From MaRDI portal
Publication:2833023
DOI10.1090/tran/6804zbMath1350.05006arXiv1309.1023OpenAlexW3100391967WikidataQ122977166 ScholiaQ122977166MaRDI QIDQ2833023
Kilian Raschel, Alin Bostan, I. A. Kurkova
Publication date: 16 November 2016
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1309.1023
generating functionselliptic functionslattice pathsalgebraic functionsenumerative combinatoricsGessel walks
Exact enumeration problems, generating functions (05A15) Compact Riemann surfaces and uniformization (30F10) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05)
Related Items
Counting quadrant walks via Tutte's invariant method, Asymptotic lattice path enumeration using diagonals, Martin boundary of killed random walks on isoradial graphs, An elementary solution of Gessel's walks in the quadrant, A decomposition of ballot permutations, pattern avoidance and Gessel walks, Encoding algebraic power series, 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, On 3-dimensional lattice walks confined to the positive octant, Continued Classification of 3D Lattice Walks in the Positive Octant, Asymptotics of lattice walks via analytic combinatorics in several variables, Counting quadrant walks via Tutte's invariant method (extended abstract), Counting walks with large steps in an orthant, Square lattice walks avoiding a quadrant, Winding of simple walks on the square lattice, Walks obeying two-step rules on the square lattice: full, half and quarter planes, Higher Dimensional Lattice Walks: Connecting Combinatorial and Analytic Behavior, A mating-of-trees approach for graph distances in random planar maps
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Walks in the quarter plane: Kreweras' algebraic model
- Explicit expression for the generating function counting Gessel's walks
- New steps in walks with small steps in the quarter plane: series expressions for the generating functions
- D-finite power series
- Classifying lattice walks restricted to the quarter plane
- Linear recurrences with constant coefficients: The multivariate case
- Proof of two conjectures of Petkovšek and Wilf on Gessel walks
- An analytical method in the theory of two-dimensional positive random walks
- Walks confined in a quadrant are not always D-finite
- On the functions counting walks with small steps in the quarter plane
- Counting walks in a quadrant: a unified approach via boundary value problems
- Walks with small steps in the quarter plane
- Proof of Ira Gessel's lattice path conjecture
- On the Holonomy or Algebraicity of Generating Functions Counting Lattice Walks in the Quarter-Plane
- Algebraic Transformations of Gauss Hypergeometric Functions
- Two Parallel Queues Created by Arrivals with Two Demands I
- The quasi-holonomic ansatz and restricted lattice walks
- Towards a human proof of Gessel's conjecture
- Two Parallel Queues Created by Arrivals with Two Demands II
- Dénombrements de chemins dans $\mathbb {R}^2$ soumis à contraintes
- Sur les périodes des intégrales doubles et sur une classe d'équations différentielles linéaires
- The complete generating function for Gessel walks is algebraic
