Guoce Xin ; Terence Y. J. Zhang
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Enumeration of bilaterally symmetric 3-noncrossing partitions
dmtcs:3613 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2008,
DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
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https://doi.org/10.46298/dmtcs.3613
Enumeration of bilaterally symmetric 3-noncrossing partitionsConference paper
Authors: Guoce Xin 1; Terence Y. J. Zhang 1
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Guoce Xin;Terence Y. J. Zhang
1 Center for Combinatorics [Nankai]
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 MAPLE package for 2-dimensional vacillating lattice walk enumeration problems. As an application, we find an interesting relation between two special bilaterally symmetric partitions.