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Counting polygon dissections in the projective plane

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hdl:2117/8343

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Noy Serrano, MarcosMés informacióMés informacióMés informació
Rué Perna, Juan JoséMés informacióMés informacióMés informació
Document typeArticle
Defense date2008-10
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
This work is protected by the corresponding intellectual and industrial property rights. Except where otherwise noted, its contents are licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
For 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.
CitationNoy, M.; Rue, J. Counting polygon dissections in the projective plane. "Advances in applied mathematics", Octubre 2008, vol. 41, núm. 4, p. 599-619. 
URIhttp://hdl.handle.net/2117/8343
ISSN0196-8858
Publisher versionhttp://www-ma2.upc.edu/noy/proj.pdf
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  • Departament de Matemàtiques - Articles de revista [3.471]
  • MD - Matemàtica Discreta - Articles de revista [75]
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