This paper constructs presentations via finite complete rewriting systems for Plactic monoids of types An, Bn, Cn, Dn, and G2, using a unified proof strategy that depends on Kashiwara’s crystal bases and analogies of Young tableaux, and on Lecouvey’s presentations for these monoids. As corollaries, we deduce that Plactic monoids of these types have finite derivation type and satisfy the homolog...

Let G be a finite group that acts on an abelian monoid A. If φ : A → G is a map so that φ(aφ(a)(b)) = φ(a)φ(b), for all a, b ∈ A, then the submonoid S = {(a, φ(a)) | a ∈ A} of the associated semidirect product A⋊G is said to be a monoid of IG-type. If A is a finitely generated free abelian monoid of rank n and G is a subgroup of the symmetric group Sym n of degree n, then these monoids first ap...

It is well known that varieties of rational languages are in one-to-one correspondence with varieties of finite monoids. This correspondence ofte., extends to operations on languages and on monoidc. We investigate the special case of the product of languages with counter, and describe the associated operations on monoids and varieties. R&emi. On sait que les varietes de IangagEs rationnels sont...

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

We prove that the classes of graded monoids, regular monoids and Kleene monoids coincide for submonoids of free groups. We also prove that it is decidable whether or not a finitely generated submonoid of a free group is graded, and solve the homomorphism and isomorphism problems for graded submonoids of free groups. This generalizes earlier results for submonoids of free monoids. MSC: 20E05; 20...

This paper studies complete rewriting systems and biautomaticity for three interesting classes of finite-rank homogeneous monoids: Chinese monoids, hypoplactic monoids, and Sylvester monoids. For Chinese monoids, we first give new presentations via finite complete rewriting systems, using more lucid constructions and proofs than those given independently by Chen & Qui and Güzel Karpuz; we then ...

A variety of finite monoids is a class of finite monoids closed under taking submonoids, quotients and finite direct products. A language L is a subset of a finitely generated free monoid. The variety theorem of Eilenberg sets up a one to one correspondence between varieties of finite monoids and classes of languages called, appropriately, varieties of languages. Recent work in variety theory h...