Generalized Stern polynomials and hyperbinary representations
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 65 (2017) no. 1, pp. 11-28
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
Karl Dilcher 1 ; Larry Ericksen 2
@article{10_4064_ba8082_2_2017,
author = {Karl Dilcher and Larry Ericksen},
title = {Generalized {Stern} polynomials and hyperbinary representations},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {11--28},
publisher = {mathdoc},
volume = {65},
number = {1},
year = {2017},
doi = {10.4064/ba8082-2-2017},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba8082-2-2017/}
}
TY - JOUR AU - Karl Dilcher AU - Larry Ericksen TI - Generalized Stern polynomials and hyperbinary representations JO - Bulletin of the Polish Academy of Sciences. Mathematics PY - 2017 SP - 11 EP - 28 VL - 65 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/ba8082-2-2017/ DO - 10.4064/ba8082-2-2017 LA - en ID - 10_4064_ba8082_2_2017 ER -
%0 Journal Article %A Karl Dilcher %A Larry Ericksen %T Generalized Stern polynomials and hyperbinary representations %J Bulletin of the Polish Academy of Sciences. Mathematics %D 2017 %P 11-28 %V 65 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/ba8082-2-2017/ %R 10.4064/ba8082-2-2017 %G en %F 10_4064_ba8082_2_2017
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
Cité par Sources :