Classifying lattice walks restricted to the quarter plane

@article{Mishna2009ClassifyingLW,
  title={Classifying lattice walks restricted to the quarter plane},
  author={M. Mishna},
  journal={J. Comb. Theory, Ser. A},
  year={2009},
  volume={116},
  pages={460-477}
}
  • M. Mishna
  • Published 2009
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
This work considers the nature of generating functions of random lattice walks restricted to the first quadrant. In particular, we find combinatorial criteria to decide if related series are algebraic, transcendental holonomic or otherwise. Complete results for walks taking their steps in a maximum of three directions of restricted amplitude are given, as is a well-supported conjecture for all walks with steps taken from a subset of {0,+/-1}^2. New enumerative results are presented for several… Expand

Figures, Tables, and Topics from this paper

Two non-holonomic lattice walks in the quarter plane
Computer Algebra in the Service of Enumerative Combinatorics
Walks with small steps in the quarter plane
Counting walks with large steps in an orthant
Infinite Orders and Non-D-finite Property of 3-Dimensional Lattice Walks
Variants of the Kernel Method for Lattice Path Models
Classification of walks in wedges
Square lattice walks avoiding a quadrant
On the Number of Walks in a Triangular Domain
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 35 REFERENCES
Two non-holonomic lattice walks in the quarter plane
Basic analytic combinatorics of directed lattice paths
Walks confined in a quadrant are not always D-finite
Walks in the quarter plane: Kreweras’ algebraic model
Walks on the slit plane
Bijective counting of Kreweras walks and loopless triangulations
  • O. Bernardi
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 2007
Partially directed paths in a wedge
Walks on the Slit Plane: Other Approaches
...
1
2
3
4
...