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13.
Stern polynomials
Klavžar, Sandi ; Milutinović, Uroš ; Petr, Ciril
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 ▫$n$▫.
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