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arXiv · 2202.00706

Row-strict dual immaculate functions

Elizabeth Niese·Sheila Sundaram·Stephanie van Willigenburg·Julianne Vega·Shiyun Wang
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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 $ψ$ 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.

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Elizabeth Niese, Sheila Sundaram, Stephanie van Willigenburg, Julianne Vega, Shiyun Wang. 2023-04-02. Row-strict dual immaculate functions. https://doi.org/10.1016/j.aam.2023.102540

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