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$q$-Stern Polynomials as Numerators of Continued Fractions

Volume 63 / 2015

Toufik Mansour Bulletin Polish Acad. Sci. Math. 63 (2015), 11-18 MSC: 11B37, 11B75, 11B83. DOI: 10.4064/ba63-1-2

Abstract

We present a $q$-analogue for the fact that the $n$th Stern polynomial $B_n(t)$ in the sense of Klav\v zar, Milutinović and Petr [Adv. Appl. Math. 39 (2007)] is the numerator of a continued fraction of $n$ terms. Moreover, we give a combinatorial interpretation for our $q$-analogue.

Authors

  • Toufik MansourDepartment of Mathematics
    University of Haifa
    3498838 Haifa, Israel
    e-mail

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