0 KB372 KB36 KB200820252012Drmota, MichaelNedela, Romanštevilka:1letnik:5str. 77-97COBISSID:16271961ISSN:1855-3966URN:URN:NBN:SI:doc-Z1M0WQTJenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneaasymptoticenumerationgrafigraphgraph theorymappreštevanjeteorija grafovzemljevidAsymptotic enumeration of reversible maps regardless of genus|We derive asymptotic expansions for the numbers ?$U(n)$? of isomorphism classes of sensed maps on orientable surfaces with given number of edges ?$n$?, where we do not specify the genus and for the numbers ?$A(n)$? of reflexible maps with ?$n$? edges. As expected the ratio ?$A(n)/U(n) \to 0$? for ?$n \to \infty$?. This shows that almost all maps are chiral. Moreover, we show ?$\log A(n) \sim \frac{1}{2} \log U(n) \sim \frac{n}{2} \log n$?. Due to a correspondence between sensed maps with given number of edges and torsion-free subgroups of the group ?$\Gamma = \langle x, y | y^2 = 1 \rangle$? of given index, the obtained results give an information on asymptotic expansions for the number of conjugacy classes of such subgroups of given indexTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije