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.

Keywords

• p-recurrence
• d-finite
• rsk-correspondence
• tableau
• partition
• [math.math-co] mathematics [math]/combinatorics [math.co]
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]