In this paper we classify all Schur functions and skew Schur functions that are multiplicity free when expanded in the basis of fundamental quasisymmetric functions, termed F -multiplicity free. Combinatorially, this is equivalent to classifying all skew shapes whose standard Young tableaux have distinct descent sets. We then generalize our setting, and classify all F -multiplicity free quasisy...

The double Schur functions form a distinguished basis of the ring Λ(x ||a) which is a multiparameter generalization of the ring of symmetric functions Λ(x). The canonical comultiplication on Λ(x) is extended to Λ(x ||a) in a natural way so that the double power sums symmetric functions are primitive elements. We calculate the dual Littlewood–Richardson coefficients in two different ways thus pr...

We establish several properties of an algorithm defined by Mason and Remmel (2010) which inserts a positive integer into a row-strict composition tableau. These properties lead to a Littlewood-Richardson type rule for expanding the product of a row-strict quasisymmetric Schur function and a symmetric Schur function in terms of row-strict quasisymmetric Schur functions. Résumé. Nous établissons ...

Several representations of the generalized Drazin inverse of an anti-triangular block matrix in Banach algebra are given in terms of the generalized Banachiewicz--Schur form.  

The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type A by a Schur function can be understood from the multiplication in the space of dual k-Schur functions. Using earlier work by the second author, we encode both problems by means of quasisymmetric functions. On the Schubert vs. Schur side, we study the r-Bruhat order given by Bergeron-Sottil...

When the parameter q ∈ C is not a root of unity, simple modules of affine q-Schur algebras have been classified in terms of Frenkel–Mukhin’s dominant Drinfeld polynomials ([6, 4.6.8]). We compute these Drinfeld polynomials associated with the simple modules of an affine q-Schur algebra which come from the simple modules of the corresponding q-Schur algebra via the evaluation maps.

The product of any finite number of Schur and factorial Schur functions can be expanded as a Z[y]-linear combination of Schur functions. We give a rule for computing the coefficients in such an expansion which generalizes the classical Littlewood-Richardson rule.