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On isomorphism classes of generalized Fibonacci cubes [Elektronski vir]
Azarija, Jernej, 1988- ...
Posplošena Fibonaccijeva kocka ▫$Q_d(f)$▫ je podgraf ▫$d$▫-kocke ▫$Q_d$▫, ki ga inducirajo nizi dolžine ▫$d$▫, ki ne vsebujejo podniza ▫$f$▫. Dokazano je, da če je ▫$Q_d(f) \cong Q_d(f')$▫, potem ...velja ▫$|f| =| f'|$▫. Ključno orodje dokaza tega izreka je rezultat Guibasa and Odlyzka o avtokorelacijskem polinomu binarnega niza. Dokazano je tudi, da obstajajo pari nizov ▫$f, f'$▫, tako da velja ▫$Q_d(f) \cong Q_d(f')$▫, kjer je ▫$|f| \ge \frac{2}{3}(d+1)$▫ in pri tem ▫$f'$▫ ne moremo dobiti iz ▫$f$▫ z invertiranjem ali binarnim komplementiranjem. Karakterizirani so tudi ▫$f$▫ in ▫$f'$▫, za katere velja ▫$|f| = |f'| = d-1$▫ in ▫$Q_d(f) \cong Q_d(f')$▫.
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