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On low-complexity bi-infinite words and their factors

Alex Heinis (2001)

Journal de théorie des nombres de Bordeaux

In this paper we study bi-infinite words on two letters. We say that such a word has stiffness k if the number of different subwords of length n equals n + k for all n sufficiently large. The word is called k -balanced if the numbers of occurrences of the symbol a in any two subwords of the same length differ by at most k . In the present paper we give a complete description of the class of bi-infinite words of stiffness k and show that the number of subwords of length n from this class has growth order...

On minimal ideals in semigroups with respect to their subsets. I.

Imrich Abrhan (1997)

Mathematica Bohemica

In the paper, the following concept are defined: (i) a minimal left (right, two-sided) ideal with respect to a subset B of a semigroup S , (ii) a kernel with respect to a subset B of a semigroup S , and their basic properties are investigated.

On modular elements of the lattice of semigroup varieties

Boris M. Vernikov (2007)

Commentationes Mathematicae Universitatis Carolinae

A semigroup variety is called modular if it is a modular element of the lattice of all semigroup varieties. We obtain a strong necessary condition for a semigroup variety to be modular. In particular, we prove that every modular nil-variety may be given by 0-reduced identities and substitutive identities only. (An identity u = v is called substitutive if the words u and v depend on the same letters and v may be obtained from u by renaming of letters.) We completely determine all commutative modular...

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