Hopf algebra structure of symmetric and quasisymmetric functions in superspace

Susanna Fishel, Luc Lapointe, María Elena Pinto

Research output: Contribution to journalArticle


We show that the ring of symmetric functions in superspace is a cocommutative and self-dual Hopf algebra. We provide formulas for the action of the coproduct and the antipode on various bases of that ring. We introduce the ring sQSym of quasisymmetric functions in superspace and show that it is a Hopf algebra. We give explicitly the product, coproduct and antipode on the basis of monomial quasisymmetric functions in superspace. We prove that the Hopf dual of sQSym, the ring sNSym of noncommutative symmetric functions in superspace, has a multiplicative basis dual to the monomial quasisymmetric functions in superspace.

Original languageEnglish (US)
Pages (from-to)144-170
Number of pages27
JournalJournal of Combinatorial Theory. Series A
Publication statusPublished - Aug 1 2019



  • Hopf algebras
  • Quasisymmetric functions
  • Superspace
  • Symmetric functions

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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