Asymptotic enumeration of reversible maps regardless of genus

作者：Drmota Michael^*; Nedela Roman

来源：Ars Mathematica Contemporanea, 2012, 5(1): 77-97.

• Graph
• map
• enumeration
• asymptotic

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) -%26gt; 0 for n -%26gt; infinity. This shows that almost all maps are chiral. Moreover, we show log A (n) similar to 1/2 log U (n) similar to (n/2) log n. Due to a correspondence between sensed maps with given number of edges and torsion-free subgroups of the group Gamma = %26lt; x, y broken vertical bar y(2) = 1 %26gt; of given index, the obtained results give an information on asymptotic expansions for the number of conjugacy classes of such subgroups of given index.

• 出版日期2012