an:00921620
Zbl 0861.20034
Mamagani, M. Dzh.
Growth functions of groups of surfaces
EN
Math. Notes 58, No. 5, 1156-1165 (1995); translation from Mat. Zametki 58, No. 5, 681-693 (1995).
00033308
1995
j
20F05 57M05 20F34 20F10 68R15 68Q42
growth functions; generating functions; minimal presentations; words; fundamental groups; closed orientable surfaces; confluent term rewriting systems
The main result is a formula for the growth function (here the generating function \(\sum d_nz^n\), where \(d_n\) is the number of the elements in a group \(G\), whose minimal presentation as words in the alphabet \(X=\{a_1,\dots,a_n,a^{-1}_1,\dots,a^{-1}_n\}\) has length \(n\)) of the fundamental group of a closed orientable surface of genus \(g\): \(G=\langle X\mid\prod^g_{i=1}[a_i,b_i]=1\rangle\). The proof uses the term rewriting approach and standard formula for calculating generating series in a confluent term rewriting system.
V.A.Ufnarovski (Lund)