Enumeration of unrooted maps of a given genus
Enumeration of unrooted maps of a given genus
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DOI：
10.1016/j.jctb.2006.01.005
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发表时间：
2006-09-01
影响因子：
1.4
通讯作者：
Nedela, Roman
中科院分区：
文献类型：
--
作者：
Mednykh, Alexander;Nedela, Roman
设N-g(F)表示亏格g的有f条边的有根映射的个数。已知N-g(F)的精确公式为g=0(Tutte，1963)，g=1(Arque，1987)，g=2，3(Bender和Canfield，1991)。本文给出了给定亏格、边数e的可定向曲面S-Gamma上无根映射的个数Theta(Gamma)(E)的计数公式.对于某个g(J)，它具有一个线性组合E-i，E-jc(i，j)N-Gj(f(I).
Let N-g (f) denote the number of rooted maps of genus g having f edges. An exact formula for N-g (f) is known for g = 0 (Tutte, 1963), g = 1 (Arques, 1987), g = 2, 3 (Bender and Canfield, 1991). In the present paper we derive an enumeration formula for the number Theta(gamma)(e) of unrooted maps on an orientable surface S-gamma of a given genus gamma and with a given number of edges e. It has a form of a linear combination E-i,E-j c(i,j) N-gj (f(i)) of numbers of rooted maps N-gj (f(i)) for some g(j)