Cycle factorizations and one-faced graph embeddings

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Consider factorizations into transpositions of an n-cycle in the symmetric group S_n. To every such factorization we assign a monomial in variables w_{ij} that retains the transpositions used, but forgets their order. Summing over all possible factorizations of n-cycles we obtain a polynomial that happens to admit a closed expression. From this expression we deduce a formula for the number of 1-faced embeddings of a given graph.
21 pages, 6 figures

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Combinatorics, Algebraic Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/221185

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0810.3892
 http://arxiv.org/abs/0810.3892

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arXiv