Geodesic
Enumeration of bilaterally symmetric 3-noncrossing partitions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008).

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Schützenberger's theorem for the ordinary RSK correspondence naturally extends to Chen et. al's correspondence for matchings and partitions. Thus the counting of bilaterally symmetric $k$-noncrossing partitions naturally arises as an analogue for involutions. In obtaining the analogous result for $3$-noncrossing partitions, we use a different technique to develop a $\mathsf{MAPLE}$ package for $2$-dimensional vacillating lattice walk enumeration problems. As an application, we find an interesting relation between two special bilaterally symmetric partitions. 
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     author = {Xin, Guoce and Zhang, Terence Y. J.},
     title = {Enumeration of bilaterally symmetric 3-noncrossing partitions},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)},
     year = {2008},
     doi = {10.46298/dmtcs.3613},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3613/}
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Xin, Guoce; Zhang, Terence Y. J. Enumeration of bilaterally symmetric 3-noncrossing partitions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008). doi : 10.46298/dmtcs.3613. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3613/

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