Journal of Combinatorics

Volume 11 (2020)

Number 1

A shifted analogue to ribbon tableaux

Pages: 169 – 202



Ezgi Kantarcı Oğuz (Department of Mathematics, University of Southern California, Los Angeles, Calif., U.S.A.)


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.

Received 20 February 2018

Published 27 September 2019