Walks with Small Steps in the 4D-Orthant

Axel Bacher, Manuel Kauers, and Rika Yatchak. Continued classification of 3d lattice walks in the positive octant. In Proceedings of FPSAC’16, pages 95–105, 2016. Olivier Bernardi, Mireille Bousquet-Mélou, and Kilian Raschel. Counting quadrant walks via Tutte’s invariant method. Technical Report, arxiv:1708.08215, 2017. Beniamin Bogosel, Vincent Perrollaz, Kilian Raschel, and Amélie Trotignon. 3d positive lattice walks and spherical triangles. Technical Report, arxiv:1807.08610, 2018. Alin Bostan. Calcul formel pour la combinatoire des marches. Habilitation a Diriger des Recherches, Universite Paris 13, 2017. Alin Bostan, Mireille Bousquet-Mélou, Manuel Kauers, and Stephen Melczer. On 3-dimensional lattice walks confined to the positive octant. Annals of Combinatorics, 20(4):661–704, 2016. Alin Bostan, Mireille Bousquet-Mélou, and Stephen Melczer. Counting walks with large steps in an orthant. Technical Report, arxiv:1806.00968, 2018. Alin Bostan, Frédéric Chyzak, Mark van Hoeij, Manuel Kauers, and Lucien Pech. Hypergeometric expressions for generating functions of walks with small steps in the quarter plane. European Journal of Combinatorics, 61:242–275, 2017. Alin Bostan and Manuel Kauers. Automatic classification of restricted lattice walks. In Proceedings of FPSAC’09, pages 201–215, 2009. Alin Bostan, Kilian Raschel, and Bruno Salvy. Non-d-finite excursions in the quarter plane. Journal of Combinatorial Theory, Series A, 121:45–63, 2014. Mireille Bousquet-Melou. Walks in the quarter plane: Kreweras’ algebraic model. The Annals of Applied Probability, 15(2):1451–1491, 2005. Mireille Bousquet-Mélou and Marni Mishna. Walks with small steps in the quarter plane. Contemporary Mathematics, 520:1–40, 2010. Julien Courtiel, Stephen Melczer, Marni Mishna, and Kilian Raschel. Weighted lattice walks and universality classes. Journal of Combinatorial Theory, Series A, 152:255–302, 2017. Thomas Dreyfus, Charlotte Hardoin, Julien Roques, and Michael F. Singer. On the nature of the generating series of walks in the quarter plane. Inventiones mathematicae, 213(1):205–236, 2018. D.K. Du, Q.-H. Hou, and R.-H. Wang. Infinite orders and non-d-finite property of 3-dimensional lattice walks. Electronic Journal of Combinatorics, 23, 2016. Guy Fayolle, Roudolf Iasnogorodski, and Vadim Malyshev. Random Walks in the quarter-plane. Springer, 1999. Charlotte Hardouin and Michael F. Singer. On differentially algebraic generating series for walks in the quarter plane. Technical Report, arxiv:2010.00963, 2020. Manuel Kauers and Peter Paule. The Concrete Tetrahedron. Springer, 2011. Manuel Kauers and Rika Yatchak. Walks in the quarter plane with multiple steps. In Proceedings of FPSAC’15, DMTCS, pages 35–36, 2015. Germain Kreweras. Sur une classe de problèmes liés au treillis des partitions d’entiers. Cahiers du B.U.R.O., 6:5–105, 1965. Irina Kurkova and Kilian Raschel. New steps in walks with small steps in the quarter plane. Annals of Combinatorics, 19:461–511, 2015. Rika Yatchak. Restricted Lattice Paths and Their Generating Functions. PhD thesis, Johannes Kepler University Linz, 2017. Richard Zippel. Effective Polynomial Computation. Springer, 1993.