TL;DR
This paper refines Sundaram's bijection between certain combinatorial objects, providing a new injection into Littlewood-Richardson Sundaram tableaux and relating it to a conjecture by Naito-Sagaki.
Contribution
It introduces a refined injection of dominant paths into Sundaram tableaux, advancing the understanding of Sundaram's bijection and its relation to Naito-Sagaki's conjecture.
Findings
Established a non-surjective injection into Sundaram tableaux
Connected the refinement to Naito-Sagaki's conjecture
Enhanced the combinatorial understanding of Sundaram's bijection
Abstract
We highlight refinement of a bijection given by Sheila Sundaram in her PhD thesis. The framework allows for comparison to a late conjecture of Naito-Sagaki. We give an injection of the set of dominant paths for this model into the corresponding set of Littlewood-Richardson Sundaram tableaux, which is not surjective. We relate this to the refinement of the aforementioned bijection.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Differential Equations and Dynamical Systems · Algebraic structures and combinatorial models