Counting polygon dissections in the projective plane

View/Open
Cita com:
hdl:2117/8343
Document typeArticle
Defense date2008-10
Rights accessOpen Access
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.
ISSN0196-8858
Publisher versionhttp://www-ma2.upc.edu/noy/proj.pdf
Collections
Files | Description | Size | Format | View |
---|---|---|---|---|
countingpolygon.pdf | 326,4Kb | View/Open |