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The covariety of perfect numerical semigroups with fixed Frobenius number

María Ángeles Moreno-Frías, José Carlos Rosales (2024)

Czechoslovak Mathematical Journal

Let S be a numerical semigroup. We say that h ∈ ℕ ∖ S is an isolated gap of S if { h - 1 , h + 1 } ⊆ S . A numerical semigroup without isolated gaps is called a perfect numerical semigroup. Denote by m ( S ) the multiplicity of a numerical semigroup S . A covariety is a nonempty family 𝒞 of numerical semigroups that fulfills the following conditions: there exists the minimum of 𝒞 , the intersection of two elements of 𝒞 is again an element of 𝒞 , and S ∖ { m ( S ) } ∈ 𝒞 for all S ∈ 𝒞 such that S ≠ min ( 𝒞 ) . We prove that the set 𝒫 ( F ) = { S : S is a perfect numerical semigroup with...

The dimension of a variety

Ewa Graczyńska, Dietmar Schweigert (2007)

Discussiones Mathematicae - General Algebra and Applications

Derived varieties were invented by P. Cohn in [4]. Derived varieties of a given type were invented by the authors in [10]. In the paper we deal with the derived variety V σ of a given variety, by a fixed hypersubstitution σ. We introduce the notion of the dimension of a variety as the cardinality κ of the set of all proper derived varieties of V included in V. We examine dimensions of some varieties in the lattice of all varieties of a given type τ. Dimensions of varieties of lattices and all subvarieties...

The Fibonacci automorphism of free Burnside groups

Ashot S. Pahlevanyan (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd n ≥ 665 and even n = 16 k ≥ 8000 .

The Fibonacci automorphism of free Burnside groups

Ashot S. Pahlevanyan (2011)

RAIRO - Theoretical Informatics and Applications

We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd n ≥ 665 and even n = 16 k ≥ 8000 .

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