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dc.contributor.authorNoy Serrano, Marcos
dc.contributor.authorRué Perna, Juan José
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.date.accessioned2010-07-22T10:49:54Z
dc.date.available2010-07-22T10:49:54Z
dc.date.created2008-10
dc.date.issued2008-10
dc.identifier.citationNoy, M.; Rue, J. Counting polygon dissections in the projective plane. "Advances in applied mathematics", Octubre 2008, vol. 41, núm. 4, p. 599-619.
dc.identifier.issn0196-8858
dc.identifier.urihttp://hdl.handle.net/2117/8343
dc.description.abstractFor each value of k ≥ 2, we determine the number pn of ways of dissecting a polygon in the projective plane into n subpolygons with k + 1 sides each. In particular, if k = 2 we recover a result of Edelman and Reiner (1997) on the number of triangulations of the MÄobius band having $\textrm{n}$ labelled points on its boundary. We also solve the problem when the polygon is dissected into subpolygons of arbitrary size. In each case, the associated generating function $\sum Pn^{{z}^{n}}$ is a rational function in $\textrm{z}$ and the corresponding generating function of plane polygon dissections. Finally, we obtain asymptotic estimates for the number of dissections of various kinds, and determine probability limit laws for natural parameters associated to triangulations and dissections.
dc.format.extent21 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
dc.subject.lcshPolygons
dc.subject.lcshProjective planes
dc.subject.lcshTriangulations
dc.subject.lcshGeometric dissections
dc.titleCounting polygon dissections in the projective plane
dc.typeArticle
dc.subject.lemacPolígons
dc.subject.lemacTriangulació
dc.subject.lemacGeometria projectiva
dc.contributor.groupUniversitat Politècnica de Catalunya. MD - Matemàtica Discreta
dc.relation.publisherversionhttp://www-ma2.upc.edu/noy/proj.pdf
dc.rights.accessOpen Access
drac.iddocument2580361
dc.description.versionPostprint (published version)
upcommons.citation.authorNoy, M.; Rue, J.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameAdvances in applied mathematics
upcommons.citation.volume41
upcommons.citation.number4
upcommons.citation.startingPage599
upcommons.citation.endingPage619


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