Structure Theorems of Mixable Shuffle Algebras

Li Guo, Bingyong Xie

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Mixable shuffle algebras are generalizations of the well-known shuffle algebra and quasi-shuffle algebra with broad applications. In this article we study the ring theoretic structures of mixable shuffle algebras with coefficients in a field motivated by the well-known work of Radford that a shuffle algebra with rational coefficients is a polynomial algebra in Lyndon words. To consider coefficients in a field of positive characteristic p, we carefully study the Lyndon words and their p-variations. As a result, we determine the structures of a quite large class of mixable shuffle algebras by providing explicit sets of generators and relations.

Original languageEnglish (US)
Pages (from-to)2629-2649
Number of pages21
JournalCommunications in Algebra
Issue number7
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


  • Lyndon words
  • Mixable shuffle
  • Polynomial
  • Quasi-shuffle
  • Shuffle

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