Row-strict dual immaculate functions

We define a new basis of quasisymmetric functions, the row-strict dual immaculate functions, as the generating function of a particular set of tableaux. We show that this definition gives a function that can also be obtained by applying the involution ψ to the dual immaculate functions of Berg, Berg...
Ausführliche Beschreibung

We define a new basis of quasisymmetric functions, the row-strict dual immaculate functions, as the generating function of a particular set of tableaux. We show that this definition gives a function that can also be obtained by applying the involution ψ to the dual immaculate functions of Berg, Bergeron, Saliola, Serrano, and Zabrocki (2014), and we establish numerous combinatorial properties for our functions. We give an equivalent formulation of our functions via Bernstein-like operators, in a similar fashion to Berg et al. (2014). We conclude the paper by defining skew dual immaculate functions and hook dual immaculate functions, and establishing combinatorial properties for them. Ausführliche Beschreibung