0 KB197 KB22 KB200820252009Nakashima, Yasuhiroštevilka:2letnik:2str. 207-215COBISSID:15498585ISSN:1855-3966URN:URN:NBN:SI:doc-OX8GNVQVenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneagrupematematikaorbiteteorija gruptranzitivnostA partial generalization of the Livingstone-Wagner Theorem|For a transitive permutation group ?$G$? on a finite set ?$\Omega$?, the Livingstone-Wagner Theorem states that if ?$G$? is ?$k$?-homogeneous and ?$2 \le k \le \frac{\vert \Omega \vert}{2}$?, then ?$G$? is ?$(k - 1)$?-transitive. We conjecture that the number of ?$G$?-orbits on ?$k$?-subsets of ?$\Omega$? is greater than or equal to the number of ?$G$?-orbits on ordered ?$(k - 1)$?-tuples of ?$\Omega$?, if ?$\vert \Omega \vert$? is sufficiently large. For the simplest case ?$k = 3$?, we verify this conjecture by establishing a result on edge-colorings of complete digraphsTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije