Balanced shifted tableaux
Jiyang Gao, Shiliang Gao, Yibo Gao

TL;DR
This paper introduces balanced shifted tableaux for root systems of type B and C, establishing a bijection with standard Young tableaux of shifted shape, thus extending combinatorial tableau theory.
Contribution
It defines balanced shifted tableaux for types B and C and proves their equinumerosity with standard Young tableaux via an explicit bijection.
Findings
Balanced shifted tableaux are introduced for types B and C.
A bijection between balanced shifted tableaux and standard Young tableaux is constructed.
Balanced shifted tableaux are shown to be equinumerous with standard Young tableaux.
Abstract
We introduce balanced shifted tableaux, as an analogue of balanced tableaux of Edelman and Greene, from the perspective of root systems of type B and C. We show that they are equinumerous to standard Young tableaux of the corresponding shifted shape by presenting an explicit bijection.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Topics in Algebra
