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In this paper, we show that all stalactic and taiga monoids of rank greater than or equal to 2 are finitely based and satisfy the same identities, that all sylvester monoids of rank greater than or equal to 2 are finitely based and satisfy the same identities and that all baxter monoids of rank greater than or equal to 2 are finitely based and satisfy the same identities. [ABSTRACT FROM AUTHOR]

Abstract Let ( hyp o n , ♯ ) be the hypoplactic monoid of finite rank n with Schützenberger’s involution ♯ . In this paper, we exhibit a faithful representation of ( hyp o n , ♯ ) as an involution monoid of upper triangular matrices over any semiring from a large class including the tropical semiring under the skew transposition. We then give a transparent combinatorial characterization of the word identities satisfied by ( hyp o n , ♯ ) . Further, we prove that ( hyp o n , ♯ ) is non-finitely based if and only if n = 2, 3 and give a polynomial time algorithm to check whether a given word identity holds in ( hyp o n , ♯ ) .Communicated by Scott Chapman [ABSTRACT FROM AUTHOR]