Row-strict dual immaculate functions

Abstract

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 establish that this definition gives a function that can also be obtained by applying the $\psi$ involution to the dual immaculate functions of Berg, Bergeron, Saliola, Serrano, and Zabrocki (2014) and 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.

32 pages. Added eqn (2.7) and Ex. 3.10, corrected eqn. (3.2), and typo in statement of Theorem 3.11. To appear in Adv. Applied Math

Cited by in corpus (5)

• 0-Hecke modules for row-strict dual immaculate functions
• Poset modules of the $0$-Hecke algebras and related quasisymmetric power sum expansions
• Pieri rules for skew dual immaculate functions
• Equivalence classes of lower and upper descent weak Bruhat intervals
• A generalization of the dual immaculate quasisymmetric functions in partially commutative variables