On the Hopf superalgebra of symmetric functions in superspace
Combinatorics
2025-09-04 v2 Mathematical Physics
math.MP
Quantum Algebra
Abstract
We introduce a superspace analogue of combinatorial Hopf algebras (Aguiar-Bergeron-Sottile, 2006), and show that the Hopf superalgebra of quasi-symmetric (resp. symmetric) functions in superspace (Fishel-Lapointe-Pinto, 2019) is a terminal object in the category of all (resp. cocommutative) combinatorial Hopf superalgebras. We also introduce a superspace analogue of chromatic symmetric functions of graphs (Stanley, 1995) using the chromatic Hopf superalgebra of two-colored graphs.
Keywords
Cite
@article{arxiv.2412.17670,
title = {On the Hopf superalgebra of symmetric functions in superspace},
author = {Masamune Hattori and Renta Yagi and Shintarou Yanagida},
journal= {arXiv preprint arXiv:2412.17670},
year = {2025}
}
Comments
14 pages,the manuscript that has been accepted for the publication in the Bulletin of the London Mathematical Society