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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 mth order Bernoulli polynomials of degree m that are Eisenstein

Arnold Adelberg, Michael Filaseta (2002)

Colloquium Mathematicae

This paper deals with the irreducibility of the mth order Bernoulli polynomials of degree m. As m tends to infinity, Eisenstein's criterion is shown to imply irreducibility for asymptotically > 1/5 of these polynomials.

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