Stern Polynomials as Numerators of Continued Fractions

• Autorzy: Schinzel A.

Identyfikatory

DOI

10.4064/ba62-1-3

• Języki publikacji: EN

Abstrakty

EN

It is proved 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. This generalizes a result of Graham, Knuth and Patashnik concerning the Stern sequence B_n(1). As an application, the degree of B_n((t) is expressed in terms of the binary expansion of n.

Słowa kluczowe

EN

Stern polynomials; continued fractions

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: Vol. 62, no 1
• Strony: 23--27
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Schinzel A.

• Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland

Bibliografia

• [1] K. Dilcher and K. B. Stolarsky, A polynomial analogue to the Stern sequence, Int. . Number Theory 3 (2007), 85-103.
• [2] R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 1994.
• [3] S. Klavžar, U. Milutinovič and C. Petr, Stern polynomials, Adv. Appl. Math. 39(2007), 86-95.
• [4] O. Perron, Die Lehre von den Kettenbruchen, 2nd ed., Teubner, 1927; reprint, Chelsea, New York, 1950.
• [5] A. Schinzel, On the factors of Stern polynomials (remarks on the preceding paper of M. Ulas), Publ. Math. Debrecen 79 (2011), 83-88.
• [6] M. Ulas, On certain arithmetic properties of Stern polynomials, Publ. Math. Debrecen 79 (2011), 55-81.
• [7] 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.