Representations and identities of plactic-like monoids

Alan J. Cain, Marianne Johnson, Mark Kambites, António Malheiro

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
4 Downloads (Pure)


We exhibit faithful representations of the hypoplactic, stalactic, taiga, sylvester, Baxter and right patience sorting monoids of each finite rank as monoids of upper triangular matrices over any semiring from a large class including the tropical semiring and fields of characteristic 0. By analysing the image of these representations, we show that the variety generated by a single hypoplactic (respectively, stalactic or taiga) monoid of rank at least 2 coincides with the variety generated by the natural numbers together with a fixed finite monoid H (respectively, F) and forms a proper subvariety of the variety generated by the plactic monoid of rank 2.

Original languageEnglish
Pages (from-to)819-850
Number of pages32
JournalJournal of Algebra
Publication statusPublished - 15 Sept 2022


  • Baxter monoid
  • Hypoplactic monoid
  • Plactic monoid
  • Representation
  • Semigroup identity
  • Stalactic monoid
  • Sylvester monoid
  • Taiga monoid
  • Tropical semiring
  • Upper triangular matrix semigroup
  • Varieties


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