# On 3-dimensional lattice walks confined to the positive octant

## Alin Bostan, Mireille Bousquet-Mélou, Manuel Kauers, Stephen Melczer

On this website we provide some code and data related to our classification project, presented
in our joint article ``On 3-dimensional lattice walks confined to the positive octant'',
ArXiv 1409.3669.
### Theory

### Code

- ThreeDSteps.mw -- Maple Worksheet containing group calculation, orbit sum calculation, generation of first terms, Hadamard decomposition for 3D models
- TwoDSteps.mw -- Maple Worksheet containing group calculation, orbit sum calculation, generation of first terms, Hadamard decomposition for 2D models
- WalksTools.m -- Collection of Mathematica functions
- dim.sage -- Sage code for recognizing redundant constraints of a step set
- Q10_is_transcendental.mpl -- Maple code for the computations in the proof of Proposition 18.

### Data

Files that are read by the Maple worksheets above:
- nonTrivial.txt -- list of all nontrivial models with ambient space Z^3, with
no unused steps, up to symmetry.
- ThreeDSteps.txt -- data set read by ThreeDSteps.mw
- TwoDSteps.txt -- data set read by TwoDSteps.mw
- results.txt -- A list of tuples (m,p,r,h,g,d), where
m is a nontrivial stepset in 3d,
p is a list of the first 25 terms of the generating function O(1,1,1,t),
r is a flag indicating whether the model can be reduced to 2d,
h is a flag indicating whether the model admits a Hadamard decomposition,
g is the order of the group (or -1 if the order exceeds 200),
d is a flag indicating whether the model is d-finite (True: provably d-finite, False: probably not d-finite)