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AuthorKlavžar, Sandi
Milutinović, Uroš
Petr, Ciril
Title Stern polynomials / Sandi Klavžar, Uroš Milutinović, Ciril Petr
Other titlesSternovi polimomi
Type/contenttype of material article - component part
LanguageEnglish
Publication date2007
Physical descriptionstr. 86-95
NotesBibliografija: str. 94-95
Uncontrolled subject headingsmatematika / 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
UDC511.217
512.622
Other class numbers
11B83 (MSC 2000)
URLhttp://dx.doi.org/10.1016/j.aam.2006.01.003
SummarySternovi 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 $n$.
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 $n$.
COBISS.SI-ID14276441
See publication: TI=Advances in applied mathematics ISSN: 0196-8858.- Vol. 39, iss. 1 (2007), str. 86-95

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