Ranking patterns of the unfolding model and arrangements

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In the unidimensional unfolding model, given m objects in general position there arise 1+m(m-1)/2 rankings. The set of rankings is called the ranking pattern of the m given objects. By changing these m objects, we can generate various ranking patterns. It is natural to ask how many ranking patterns can be generated and what is the probability of each ranking pattern when the objects are randomly chosen? These problems are studied by introducing a new type of arrangement called mid-hyperplane arrangement and by counting cells in its complement.
29 pages, 2 figures

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Combinatorics, Probability, 05C90

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http://salesiana.dossiersoluciones.com/handle/123456789/133310

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0404343
 http://arxiv.org/abs/math/0404343
 Annals of Combinatorics, 10 (2006), 219-235

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arXiv