A Relation Between Schröder Paths and Motzkin Paths
A Relation Between Schröder Paths and Motzkin Paths
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DOI：
10.1007/s00373-020-02185-6
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发表时间：
2020-05
影响因子：
0.7
通讯作者：
Lin Yang;Sheng-Liang Yang
中科院分区：
文献类型：
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作者：
Lin Yang;Sheng-Liang Yang
一条半长度的smallq-Schröder路径是一条从（0,0）到（2n, 0）的点阵路径，它使用上阶、水平阶和下阶，这样它就会弱地停留在x轴之上，在x轴上没有水平阶，并且每个水平阶都有不同的颜色。本文给出了半长度的smallq-Schröder路径集与长度为n的of- motzkin路径集之间的双射。此外，还得到了半长度的小3-Schröder路径集与半长度的Catalan rok路径集之间的一一对应关系，以及小4-Schröder路径与Catalan queen路径之间的双映射关系。
A smallq-Schröder path of semilengthnis a lattice path from (0, 0) to (2n, 0) using up steps, horizontal steps, and down stepssuch that it stays weakly above thex-axis, has no horizontal steps on thex-axis, and each horizontal step comes inqcolors. In this paper, we provide a bijection between the set of smallq-Schröder paths of semilengthand the set of-Motzkin paths of lengthn. Furthermore, a one-to-one correspondence between the set of small 3-Schröder paths of semilengthnand the set of Catalan rook paths of semilengthnis obtained, and a bijection between small 4-Schröder paths and Catalan queen paths is also presented.