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Enumeration of bilaterally symmetric 3-noncrossing partitions

Abstract : 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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Guoce Xin, Terence Y. J. Zhang. Enumeration of bilaterally symmetric 3-noncrossing partitions. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.705-716. ⟨hal-01185147⟩

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