Title: Bijections among symmetric tableaux via folding and mixed insertion
|Affiliation:||University of Waterloo|
A standard Young tableau with entries $-M < \cdots -1 < 1 < \cdots < M$ can be "folded" by performing certain conversions and rectifications in sequence. This operation yields a tableau with entries $1' < 1 < \cdots < M' < M$ and has a remarkable relationship to a generalization of Schensted insertion known as "mixed insertion". Using a connection between domino insertion and mixed insertion, we can show that folding yields a bijection between certain tableaux with rotational symmetry (obtained from specific shifted tableaux) and symmetric domino tableaux (that are in one-to-one correspondence with standard square tableaux). Similar bijections arise when considering other symmetries, some of which admit geometric explanations.
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