Cycle factorizations and one-faced graph embeddings

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dc.creatorBurman, Yurii
dc.creatorZvonkine, Dimitri
dc.date2008-10-21
dc.date2009-02-24
dc.date.accessioned2026-07-07T12:45:51Z
dc.date.available2026-07-07T12:45:51Z
dc.descriptionConsider 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.
dc.description21 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/0810.3892
dc.identifierhttp://arxiv.org/abs/0810.3892
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221185
dc.subjectCombinatorics
dc.subjectAlgebraic Geometry
dc.titleCycle factorizations and one-faced graph embeddings
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