Divergence zero quaternionic vector fields and Hamming graphs
Prezelj, Jasna ; Vlacci, Fabio
V članku je predlagana možna razširitev definicije kvaternionskih potenčnih vrst, parcialnih odvodov in vektorskih polj za dve oz. več nekomutativnih (kvaternionskih) spremenljivk. Obravnavan je ...problem ničelnih funkcij, ki jih popisujejo vrste, ki niso formalno ničelne. Podana je povezava med analitičnim pogojem in pogojem na podgraf Hammingovega grafa. Natančneje, polinomsko vektorsko polje ima formalno divergenco nič natanko tedaj, ko je določen podgraf Hammingovega grafa ▫$H(d, 2)$▫ povezan. Dokazano je, da so monomi v spremenljivkah ▫$z$▫ in ▫$w$▫ vedno linearno neodvisni kot funkcije samo v bistopnjah ▫$(p, 0)$▫, ▫$(p, 1)$▫, ▫$(0, q)$▫, ▫$(1, q)$▫ in ▫$(2, 2)$▫.
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