Manuel Kauers ; Rika Yatchak - Walks in the Quarter Plane with Multiple Steps

dmtcs:2463 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) - https://doi.org/10.46298/dmtcs.2463
Walks in the Quarter Plane with Multiple StepsArticle

Authors: Manuel Kauers 1; Rika Yatchak 1

  • 1 Research Institute for Symbolic Computation

We extend the classification of nearest neighbour walks in the quarter plane to models in which multiplicities are attached to each direction in the step set. Our study leads to a small number of infinite families that completely characterize all the models whose associated group is D4, D6, or D8. These families cover all the models with multiplicites 0, 1, 2, or 3, which were experimentally found to be D-finite — with three noteworthy exceptions.


Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Imported on: November 21, 2016
Keywords: Computer Algebra,Lattice Walks,D-finiteness,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Fast Computer Algebra for Special Functions; Funder: Austrian Science Fund (FWF); Code: Y 464

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