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Some infinite products with interesting continued fraction expansions

C. G. Pinner, A. J. Van der Poorten, N. Saradha (1993)

Journal de théorie des nombres de Bordeaux

We display several infinite products with interesting continued fraction expansions. Specifically, for various small values of k necessarily excluding k = 3 since that case cannot occur, we display infinite products in the field of formal power series whose truncations yield their every k -th convergent.

The code problem for directed figures

Michał Kolarz (2010)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We consider directed figures defined as labelled polyominoes with designated start and end points, with two types of catenation operations. We are especially interested in codicity verification for sets of figures, and we show that depending on the catenation type the question whether a given set of directed figures is a code is decidable or not. In the former case we give a constructive proof which leads to a straightforward algorithm.

The code problem for directed figures

Michał Kolarz (2011)

RAIRO - Theoretical Informatics and Applications

We consider directed figures defined as labelled polyominoes with designated start and end points, with two types of catenation operations. We are especially interested in codicity verification for sets of figures, and we show that depending on the catenation type the question whether a given set of directed figures is a code is decidable or not. In the former case we give a constructive proof which leads to a straightforward algorithm.

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