A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Generalized Stern polynomials and hyperbinary representations

Volume 65 / 2017

Karl Dilcher, Larry Ericksen Bulletin Polish Acad. Sci. Math. 65 (2017), 11-28 MSC: Primary 05A15; Secondary 11B83. DOI: 10.4064/ba8082-2-2017 Published online: 17 March 2017

Abstract

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.

Authors

  • Karl DilcherDepartment of Mathematics and Statistics
    Dalhousie University
    Halifax, Nova Scotia, B3H 4R2, Canada
    e-mail
  • Larry EricksenP.O. Box 172
    Millville, NJ 08332-0172, U.S.A.
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image