Expanding quasisymmetric Schur $Q$-functions into peak Young quasisymmetric Schur functions

TL;DR

This paper demonstrates that quasisymmetric Schur Q-functions can be expanded into peak Young quasisymmetric Schur functions with nonnegative coefficients, revealing a new connection between these bases in the peak algebra.

Contribution

It establishes the nonnegative expansion of quasisymmetric Schur Q-functions into peak Young quasisymmetric Schur functions, linking two important bases in the peak algebra.

Findings

Nonnegative expansion coefficients established

Connection between dual immaculate and peak algebra bases

Enhances understanding of quasisymmetric function bases

Abstract

The dual immaculate and Young quasisymmetric Schur bases of quasisymmetric functions possess analogues in the peak algebra: respectively, the quasisymmetric Schur $Q$-functions and the peak Young quasisymmetric Schur functions. We show elements of the former basis expand into the latter basis with nonnegative coefficients.