Continued fractions and polynomials related to hyperbinary representations

Schinzel recently showed that the nth Stern polynomial of Klavžar et al. is the numerator of a certain finite continued fraction. This was subsequently extended by Mansour to q-Stern polynomials. We extend these results further to a 2-parameter bivariate analogue of the sequence of Stern polynomials which arise naturally in the characterization of hyperbinary representations of a given integer. In the process we define a class of companion polynomials with which we can determine the denominators of the continued fractions in question.

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Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).