In this paper we generalize the results obtained in [1] and [2] for the determination of the Hausdorff dimension of the univoque set. We break down the general problem into two subcases, and accomplish the investigation completely in the simplest case. Finally we illustrate the theoretical results with an interesting example.

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In this paper we continue the investigation of the numbers which have only one expansion in the formWe present a method for the determination of the Hausdorff dimension of the set of these numbers in the so-called big case, illustrated with interesting examples.

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In this paper we generalize the Pascal triangle and examine the connections among the generalized triangles and powering integers respectively polynomials. We emphasize connections with the binomial and multinomial theorems, and finally we present some computational results.