Identities for vacillating tableaux via growth diagrams

TL;DR

This paper presents bijective proofs using Fomin's growth diagrams to establish identities involving vacillating tableaux, connecting combinatorial structures with representation theory of partition algebras.

Contribution

It introduces a novel bijective approach employing growth diagrams to prove identities related to vacillating tableaux, expanding combinatorial methods in algebraic contexts.

Findings

Established new bijective proofs for vacillating tableaux identities

Connected combinatorial proofs with representation theory concepts

Enhanced understanding of tableau enumeration through growth diagrams

Abstract

We give bijective proofs using Fomin's growth diagrams for identities involving numbers of vacillating tableaux that arose in the representation theory of partition algebras or are inspired by such identities.