# A Type B Analogue to Ribbon Tableaux

## TL;DR

This paper introduces a shifted analogue of ribbon tableaux, establishing a bijection with certain shape fillings, and proves their generating functions are symmetric and positive in Schur and Schur Q-terms.

## Contribution

It presents a new shifted analogue of ribbon tableaux, along with a bijection and properties of their generating functions, extending classical tableau theory.

## Key findings

- Bijection between k-ribbon fillings and k-quotients of shapes.
- Generating functions are symmetric and Schur positive.
- Generating functions are also Schur Q-positive.

## Abstract

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 also define the corresponding generating functions, and prove that they are symmetric, Schur positive and Schur $Q$-positive.