Walks with small steps in the quarter plane

@article{BousquetMlou2008WalksWS,
  title={Walks with small steps in the quarter plane},
  author={M. Bousquet-M{\'e}lou and Marni Mishna},
  journal={arXiv: Combinatorics},
  year={2008}
}
  • M. Bousquet-Mélou, Marni Mishna
  • Published 2008
  • Mathematics
  • arXiv: Combinatorics
  • Let S be a subset of {-1,0,1}^2 not containing (0,0). We address the enumeration of plane lattice walks with steps in S, that start from (0,0) and always remain in the first quadrant. A priori, there are 2^8 problems of this type, but some are trivial. Some others are equivalent to a model of walks confined to a half-plane: such models can be solved systematically using the kernel method, which leads to algebraic generating functions. We focus on the remaining cases, and show that there are 79… CONTINUE READING

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