Identities and bases in the hypoplactic monoid

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This paper presents new results on the identities satisfied by the hypoplactic monoid. We show how to embed the hypoplactic monoid of any rank strictly greater than 2 (including infinite rank) into a direct product of copies of the hypoplactic monoid of rank 2. This confirms that all hypoplactic monoids of rank greater than or equal to 2 satisfy exactly the same identities. We then give a complete characterization of those identities, and prove that the variety generated by the hypoplactic monoid has finite axiomatic rank, by giving a finite basis for it.

Original languageEnglish
Pages (from-to)146-162
JournalCommunications in Algebra
Issue number1
Publication statusPublished - 17 Jan 2022


  • axiomatic rank
  • equational basis
  • Hypoplactic monoid
  • identities
  • variety


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