Ranking patterns of the unfolding model and arrangements

Details Ranking patterns of the unfolding model and arrangements Ranking patterns of the unfolding model and arrangements

2004-04-19

arxiv.org/abs/math/0404343v1

Annals of Combinatorics, 10 (2006), 219-235

Mathematics

Combinatorics

29 pages, 2 figures

Scientific paper

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.

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