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Row-strict dual immaculate functions

Authors :
Niese, Elizabeth
Sundaram, Sheila
van Willigenburg, Stephanie
Vega, Julianne
Wang, Shiyun
Source :
Advances in Applied Mathematics 149 (2023) 102540
Publication Year :
2022

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.<br />Comment: 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

Details

Database :
arXiv
Journal :
Advances in Applied Mathematics 149 (2023) 102540
Publication Type :
Report
Accession number :
edsarx.2202.00706
Document Type :
Working Paper
Full Text :
https://doi.org/10.1016/j.aam.2023.102540