Stern polynomials

Sandi Klavžar (Author), Uroš Milutinović (Author), Ciril Petr (Author)

Abstract

Sternovi polinomi ▫$B_k(t)$▫, ▫$k \ge 0$▫, ▫$t \in \RR$▫, so vpeljani na naslednji način: ▫$B_0(t) = 0$▫, ▫$B_1(t) = 1$▫, ▫$B_{2n}(t) = tB_n(t)$▫ in ▫$B_{2n+1}(t) = B_{n+1}(t) + B_n(t)$▫. Pokazano je, da ima ▫$B_n(t)$▫ enostavno eksplicitno reprezentacijo s hiperebinarnimi reprezentacijami ▫$n-1$▫ in da je odvod ▫$B'_{2n-1}(0)$▫ enak številu enic v standardni Grayjevi kodi za ▫$n-1$▫. Dokazano je tudi, da je stopnja polinoma ▫$B_n(t)$▫ enaka razliki med dolžino in težo nesosednje predstavitve števila ▫$n$▫.

Keywords

matematika;Sternovo (dvoatomsko) zaporedje;Sternovi polinomi;hiperbinarna reprezentacija;standardna Grayjeva koda;nesosednja predstavitev;mathematics;Stern (diatomic) sequence;Stern polynomials;hyperbinary representation;standard Gray code;non-adjacent form;

Data

Language:	English
Year of publishing:	2007
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	511.217
COBISS:	14276441
ISSN:	0196-8858
Views:	834
Downloads:	25
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Unknown
Secondary title:	Sternovi polimomi
Secondary abstract:	Stern polynomials ▫$B_k(t)$▫, ▫$k \ge 0$▫, ▫$t \in \RR$▫, are introduced in the following way: ▫$B_0(t) = 0$▫, ▫$B_1(t) = 1$▫, ▫$B_{2n}(t) = tB_n(t)$▫, and ▫$B_{2n+1}(t) = B_{n+1}(t) + B_n(t)$▫. It is shown that ▫$B_n(t)$▫ has a simple explicit representation in terms of the hyperbinary representations of ▫$n-1$▫ and that ▫$B'_{2n-1}(0)$▫ equals the number of 1's in the standard Gray code for ▫$n-1$▫. It is also proved that the degree of ▫$B_n(t)$▫ equals the difference between the length and the weight of the non-adjacent form of ▫$n$▫.
Secondary keywords:	matematika;Sternovo (dvoatomsko) zaporedje;Sternovi polinomi;hiperbinarna reprezentacija;standardna Grayjeva koda;nesosednja predstavitev;
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 86-95
Volume:	ǂVol. ǂ39
Issue:	ǂiss. ǂ1
Chronology:	2007
ID:	1473053