q-Stern Polynomials as Numerators of Continued Fractions

• Autorzy: Mansour T.

Identyfikatory

DOI

10.4064/ba63-1-2

• Języki publikacji: EN

Abstrakty

EN

We present a q-analogue for the fact that the nth Stern polynomial B_n(t) in the sense of Klavžar, 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.

Słowa kluczowe

EN

Stern polynomial; q-analogue; hyperbinary expansion; continued fraction

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2015
• Tom: Vol. 63, no. 1
• Strony: 11--18
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Mansour T.

• Department of Mathematics, University of Haifa, 3498838 Haifa, Israel

Bibliografia

• [1] B. Bates, M. Bunder and K. Tognetti, Linking the Calkin-Wilf and Stern-Brocot trees, Eur. J. Combin. 31 (2010), 1637-1661.
• [2] B. Bates and T. Mansour, The q-Calkin-Wilf tree, J. Combin. Theory Ser. A 118 (2011), 1143-1151.
• [3] N. Calkin and H. S. Wilf, Recounting the rationals, Amer. Math. Monthly 107 (2000), 360-363.
• [4] K. Dilcher and K. B. Stolarsky, A polynomial analogue to the Stern sequence, Int. J. Number Theory 3 (2007), 85-103.
• [5] R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 1994.
• [6] S. Klavžar, U. Milutinović and C. Petr, Stern polynomials, Adv. Appl. Math. 39 (2007), 86-95.
• [7] O. Perron, Die Lehre von den Kettenbrüchen, 2nd ed., Teubner, 1927; reprint, Chelsea, New York, 1950.
• [8] A. Schinzel, Stern polynomials as numerators of continued fractions, Bull. Polish Acad. Sci. Math. 62 (2014), 23-27.
• [9] M. Ulas, On certain arithmetic properties of Stern polynomials, Publ. Math. Debrecen 79 (2011), 55-81.
• [10] I. Urbiha, Some properties of a function studied by de Rham, Carlitz and Dijkstra and its relation to the (Eisenstein-)Stern's diatomic sequence, Math. Comm. 6 (2001), 181-198.