A shifted analogue to ribbon tableaux

We introduce a shifted analogue of the ribbon tableaux defined by James and Kerber. For any positive integer $k$, we give a bijection between the $k$-ribbon fillings of a shifted shape and regular fillings of a $\lfloor k/2 \rfloor$-tuple of shapes called its $k$-quotient. We define the corresponding generating functions, and prove that they are symmetric, Schur positive and Schur $Q$-positive. Then we introduce a Schur $Q$-positive $q$-refinement.

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Received 20 February 2018

Published 27 September 2019