20.500.12556/DKUM-49373 Stern polynomials Sternovi polimomi 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 ▫$n$▫. 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 ▫$n$▫. 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 true false false Angleški jezik Neznan jezik Delo ni kategorizirano 2015-07-10 12:00:22 2015-07-10 12:00:22 2022-05-27 03:09:27 2019-07-10 21:28:21 2005 0 0 str. 1-11 št. 994 Vol. 43 2005 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 1318-4865 511.217 44310272 13805913 URN:SI:UM:DK:22K1ZGTT http://www.imfm.si/preprinti/PDF/00994.pdf 1 https://dk.um.si/Dokument.php?lang=slv&id=73932 Pedagoška fakulteta 0 0 0