Year: 2025
Type: preprint
Abstract: John M. Campbell constructed a combinatorial Hopf algebra (CHA) \text{ParSym} on partition diagrams by lifting the CHA structure of \text{NSym} (the Hopf algebra of noncommutative symmetric functions) through an analogous approach. In this article, we define \text{ParQSym}, which is the graded dual of \text{ParSym}. Its CHA structure is defined in an explicit, combinatorial way, by analogy with that of the CHA \text{QSym} of quasisymmetric functions. And we give some subcoalgebra and Hopf subalgebras of \text{ParQSym}, some gradings and filtrations of \text{ParSym} and \text{ParQSym}, and some bases of \text{ParSym} and \text{ParQSym} by analogy with some distinguished bases of \text{NSym} and \text{QSym}.
Source: arXiv (Cornell University)
Authors: Hao, Lingxiao, Zhu, Shenglin
Institution: Fudan University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979319052
Cites:
Cited by:
Related to: