Motivated by the study of Macdonald polynomials, J. Haglund and A. Wilson introduced a nonsymmetric polynomial analogue chromatic quasisymmetric function called chromatic polynomial Dyck graph. We give positive expansion for this in basis fundamental slide polynomials using recent work Assaf-Bergeron on flagged <mml:math xmlns:mml="ht...

With techniques borrowed from quantum information theory, we develop a method to systematically obtain operator inequalities and identities in several matrix variables. These take the form of trace polynomials: polynomial-like expressions that involve monomials Xα1,…,Xαr their traces tr(Xα1,…,Xαr). Our rests on translating action symmetric group tensor product spaces into multiplication. As res...