We establish an extension of Viennot’s geometric (shadow line) construction to the setting of oscillating tableaux. We then use this to give a new proof of the Type C analogue of Schensted’s theorem on longest decreasing subsequences. This pairs with our results from 3 on Type C webs to 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 sp₂₍ equals the number of (n+1) -avoiding matchings of 2k points.
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Bodish et al. (Mon,) studied this question.
www.synapsesocial.com/papers/69ba42cf4e9516ffd37a369b — DOI: https://doi.org/10.1007/s12188-026-00295-1
Elijah Bodish
Ben Elias
D. Roderick Rose
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
University of North Carolina at Chapel Hill
Indiana University Bloomington
University of Oregon
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