0 KB364 KB51 KB200820252011Jones, Gareth A.številka:2letnik:4str. 313-328COBISSID:16268121ISSN:1855-3966URN:URN:NBN:SI:doc-NGNF8UPQenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneaautomorphism groupGalois groupGaloisova grupagrupa avtomorfizmovHamming graphHamming mapHammingova preslikavaHammingovi grafiClassification and Galois conjugacy of Hamming maps|We show that for each ?$d \ge 1$? the ?$d$?-dimensional Hamming graph ?$H(d, q)$? has an orientably regular surface embedding if and only if ?$q$? is a prime power ?$p^e$?. If ?$q > 2$? there are up to isomorphism ?$\phi(q - 1)/e$? such maps, all constructed as Cayley maps for a ?$d$?-dimensional vector space over the field ?$F_q$?. We show that for each such pair ?$(d, q)$? the corresponding Belyi pairs are conjugate under the action of the absolute Galois group Gal ?$\overline{\mathbf Q}$?, and we determine their minimal field of definition. We also classify the orientably regular embedding of merged Hamming graphs for ?$q > 3$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije