Geodesic
Generalized Stern polynomials and hyperbinary representations
Karl Dilcher 1   ; Larry Ericksen 2
1 Department of Mathematics and Statistics Dalhousie University Halifax, Nova Scotia, B3H 4R2, Canada
2 P.O. Box 172 Millville, NJ 08332-0172, U.S.A.
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 65 (2017) no. 1, pp. 11-28 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We use two different but related types of generalized Stern polynomials, recently introduced by the authors, to give complete characterizations of all hyperbinary expansions of a given positive integer. We also derive explicit formulas for these generalized Stern polynomials and use them to establish further characterizations of hyperbinary expansions, using binomial coefficients. We then introduce a 2-parameter analogue of the two types of polynomials, which leads to more explicit versions of earlier results. Finally, we explore further generalizations of the polynomials studied in this paper.
DOI : 10.4064/ba8082-2-2017
Keywords: different related types generalized stern polynomials recently introduced authors complete characterizations hyperbinary expansions given positive integer derive explicit formulas these generalized stern polynomials establish further characterizations hyperbinary expansions using binomial coefficients introduce parameter analogue types polynomials which leads explicit versions earlier results finally explore further generalizations polynomials studied paper

Karl Dilcher  1   ; Larry Ericksen  2

1 Department of Mathematics and Statistics Dalhousie University Halifax, Nova Scotia, B3H 4R2, Canada
2 P.O. Box 172 Millville, NJ 08332-0172, U.S.A. 
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     title = {Generalized {Stern} polynomials and hyperbinary representations},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
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Karl Dilcher; Larry Ericksen. Generalized Stern polynomials and hyperbinary representations. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 65 (2017) no. 1, pp. 11-28. doi: 10.4064/ba8082-2-2017

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