Geodesic
From \((2,3)\)-Motzkin paths to Schröder paths
Journal of integer sequences, Tome 10 (2007) no. 9
In this paper, we provide a bijection between the set of restricted (2,3)-Motzkin paths of length $n$ and the set of Schröder paths of semilength $n$. Furthermore, we give a one-to-one correspondence between the set of (2,3)-Motzkin paths of length $n$ and the set of little Schröder paths of semilength $n+1$. By applying the bijections, we get the enumerations of Schröder paths according to the statistics "number of $udd$'s" and "number of $hd$'s".
Classification : 05A15, 05A19
Keywords: schr$\ddot $oder path, (2, 3)-Motzkin path 
@article{JIS_2007__10_9_a0,
     author = {Yan,  Sherry H.F.},
     title = {From {\((2,3)\)-Motzkin} paths to {Schr\"oder} paths},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {9},
     zbl = {1143.05005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_9_a0/}
}
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%A Yan,  Sherry H.F.
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%J Journal of integer sequences
%D 2007
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Yan,  Sherry H.F. From \((2,3)\)-Motzkin paths to Schröder paths. Journal of integer sequences, Tome 10 (2007) no. 9. http://geodesic.mathdoc.fr/item/JIS_2007__10_9_a0/