# A note on the Sundaram--Stanley bijection (or, Viennot for up-down tableaux)

@inproceedings{Bodish2021ANO, title={A note on the Sundaram--Stanley bijection (or, Viennot for up-down tableaux)}, author={Elijah Bodish and Ben Elias and David E. V. Rose and Logan C. Tatham}, year={2021} }

We give a direct proof of a result of Sundaram and Stanley: that the dimension of the space of invariant vectors in a 2k-fold tensor product of the vector representation of sp2n equals the number of (n+1)-avoiding matchings of 2k points. This can be viewed as an extension of Schensted’s theorem on longest decreasing subsequences. Our main tool is an extension of Viennot’s geometric construction to the setting of up-down tableaux.

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