On the Hopf superalgebra of symmetric functions in superspace

2024/12/23 by Masamune Hattori, Hattori, Masamune, Renta Yagi +3
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2412.17670

openalex publication_date 2024/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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