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On Lattice Paths with Four Types of Steps

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Abstract

In this paper, we give a bijective proof of an identity on lattice paths with four types of steps in answer to a problem posed by Dziemiańczuk. Moreover, we prove a bijective relationship between the number of positive lattice paths and \(m\)-flawed lattice paths.

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Acknowledgments

The authors are very grateful to the referee for their comments and suggestions which helped to improve the presentation of the paper. This work was supported by the National Natural Science Foundation of China and ZJNSF (No. Y14A010029).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Sherry H. F. Yan & Yaqiu Zhang

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  1. Sherry H. F. Yan
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  2. Yaqiu Zhang
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Correspondence to Sherry H. F. Yan.

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Yan, S.H.F., Zhang, Y. On Lattice Paths with Four Types of Steps. Graphs and Combinatorics 31, 1077–1084 (2015). https://doi.org/10.1007/s00373-014-1424-2

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  • DOI: https://doi.org/10.1007/s00373-014-1424-2

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