Work

Decreasing subsequences and Viennot for oscillating tableaux

Year: 2025

Type: article

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 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 2 k -fold tensor product of the vector representation of $$\mathfrak {sp}_{2n}$$ equals the number of $$(n+1)$$ -avoiding matchings of 2 k points.

Source: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

DOI: 10.1007/s12188-026-00295-1

Authors: Elijah Bodish, Ben Elias, David E. V. Rose, Logan Tatham

Institutions: Indiana University Bloomington, Indiana University, University of Oregon, University of North Carolina at Chapel Hill

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: National Science Foundation