Geodesic
Infinite orders and non-\(D\)-finite property of 3-dimensional lattice walks
Daniel K. Du1 ; Qing-Hu Hou1 ; Rong-Hua Wang2
1Tianjin University
2Nankai University
The electronic journal of combinatorics, Tome 23 (2016) no. 3
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Recently, Bostan and his coauthors investigated lattice walks restricted to the non-negative octant $\mathbb{N}^3$. For the $35548$ non-trivial models with at most six steps, they found that many models associated to a group of order at least $200$ and conjectured these groups were in fact infinite groups. In this paper, we first confirm these conjectures and then consider the non-$D$-finite property of the generating function for some of these models.
DOI : 10.37236/5408
Classification : 05A15, 60G50
Mots-clés : lattice walks, generating functions, \(D\)-finite

Daniel K. Du  1   ; Qing-Hu Hou  1   ; Rong-Hua Wang  2

1 Tianjin University
2 Nankai University 
@article{10_37236_5408,
     author = {Daniel K. Du and Qing-Hu Hou and Rong-Hua Wang},
     title = {Infinite orders and {non-\(D\)-finite} property of 3-dimensional lattice walks},
     journal = {The electronic journal of combinatorics},
     year = {2016},
     volume = {23},
     number = {3},
     doi = {10.37236/5408},
     zbl = {1344.05013},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/5408/}
}
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Daniel K. Du; Qing-Hu Hou; Rong-Hua Wang. Infinite orders and non-\(D\)-finite property of 3-dimensional lattice walks. The electronic journal of combinatorics, Tome 23 (2016) no. 3. doi: 10.37236/5408

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