Enumeration of maps regardless of genus: Geometric approach
نویسندگان
چکیده
منابع مشابه
Enumeration of maps regardless of genus: Geometric approach
We use the conceptual idea of “maps on orbifolds” and the theory of the nonEuclidian crystallographic groups (NEC groups) to enumerate rooted and unrooted maps (both sensed and unsensed) on surfaces regardless of genus. As a consequence we deduce a formula for the number of chiral pairs of maps. The enumeration principle used in this paper is due to A. D. Mednykh (2006), it counts the number of...
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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) → 0 for n → ∞. This shows that almost all maps are chiral. Moreover, we show logA(n) ∼ 12 logU(n) ∼ (n/2) log n. Due to a corresp...
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Let Ng(f) denote the number of rooted maps of genus g having f edges. Exact formula for Ng(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 Θγ(e) of unrooted maps on an orientable surface Sγ of given genus γ and given number of edges e. It has a form of a linear combination ∑ i,j ci...
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Let Ng(f ) denote the number of rooted maps of genus g having f edges. An exact formula for Ng(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 Θγ (e) of unrooted maps on an orientable surface Sγ of a given genus γ and with a given number of edges e. It has a form of a linear com...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.11.017