Decreasing subsequences and Viennot for oscillating tableaux
Combinatorics
2026-01-16 v2 Representation Theory
Abstract
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 analogue of Schensted's theorem on longest decreasing subsequences. This pairs with our results from arXiv:2103.14997v1 [math.RT] on Type webs to give a direct proof of a result of Sundaram and Stanley: that the dimension of the space of invariant vectors in a -fold tensor product of the vector representation of equals the number of -avoiding matchings of points.
Cite
@article{arxiv.2108.11528,
title = {Decreasing subsequences and Viennot for oscillating tableaux},
author = {Elijah Bodish and Ben Elias and David E. V. Rose and Logan Tatham},
journal= {arXiv preprint arXiv:2108.11528},
year = {2026}
}
Comments
16 pages, many diagrams, color viewing essential, final version (to appear in Abh. Math. Semin. Univ. Hambg.)