460 KB30 KB200820252016Berman, LeahHoef, Lander VerJacksch, Elliottletnik:10številka:2str. 411-425COBISSID:17835609ISSN:1855-3966URN:URN:NBN:SI:doc-7AH7S5PNenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneaconfigurationsincidence geometryincidenčna geometrijakonfiguracijeAn infinite class of movable 5-configurations|A geometric 5-configuration is a collection of points and straight lines, typically in the Euclidean plane, in which every point has 5 lines passing through it and every line has 5 points lying on it; that is, it is an ?$(n_5)$? configuration for some number ?$n$? of points and lines. Using reduced Levi graphs and two elementary geometric lemmas, we develop a construction that produces infinitely many new 5-configurations which are movable; in particular, we produce infinitely many 5-configurations with one continuous degree of freedom, and we produce 5-configurations with ?$k-2$? continuous degrees of freedom for all odd ?$k > 2$?Geometrijska 5-konfiguracija je sestav točk in premic v evklidski ravnini, v kateri gre skozi vsako točko 5 premic, na vsaki premici pa leži 5 točk; to je torej ?$(n_5)$? kon- figuracija za neko število ?$n$? točk in premic. Z uporabo reduciranih Levijevih grafov in dveh elementarnih geometrijskih lem razvijemo konstrukcijo, ki nam da neskončno mnogo novih in gibljivih 5-konfiguracij; na ta način dobimo neskončno mnogo 5-konfiguracij z eno zvezno prostostno stopnjo, pa tudi 5-konfiguracije s ?$k - 2$? zveznimi prostostnimi stopnjami za vse lihe ?$k > 2$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije