Powersum Bases in Quasisymmetric Functions and Quasisymmetric Functions in Non-commuting Variables
Combinatorics
2021-12-28 v1
Abstract
We introduce new bases for the Hopf algebra of quasisymmetric functions that refine the symmetric powersum basis. These bases are expanded in terms of quasisymmetric monomial functions by using fillings of matrices. We define the analog of these bases in quasisymmetric functions of non-commuting variables. Our new bases have a (shifted) shuffle product and a deconcatenate coproduct. Finally, we describe a change of basis rule from the quasisymmetric powersum basis to the quasisymmetric fundamental basis.
Keywords
Cite
@article{arxiv.2112.13333,
title = {Powersum Bases in Quasisymmetric Functions and Quasisymmetric Functions in Non-commuting Variables},
author = {Anthony Lazzeroni},
journal= {arXiv preprint arXiv:2112.13333},
year = {2021}
}
Comments
This is an extended abstract submitted to FPSAC 2022