Positive expansions of extended Schur functions in the Young quasisymmetric Schur basis

There are a number of Schur -like bases for the quasisymmetric functions. Extended Schur functions, introduced by Assaf and Searles, expand positively in the Young quasisymmetric Schur basis for certain indexing compositions. We establish this expansion using an algorithm defined by Allen, Hallam, and Mason restricted to the generating objects of the extended Schur functions.