Abstract.
In the unidimensional unfolding model, given m objects in general position on the real line, there arise 1 + m(m − 1)/2 rankings. The set of rankings is called the ranking pattern of the m given objects. Change of the position of these m objects results in change of the ranking pattern. In this paper we use arrangement theory to determine the number of ranking patterns theoretically for all m and numerically for m ≤ 8. We also consider the probability of the occurrence of each ranking pattern when the objects are randomly chosen.
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Received March 5, 2005
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Kamiya, H., Orlik, P., Takemura, A. et al. Arrangements and Ranking Patterns. Ann. Comb. 10, 219–235 (2006). https://doi.org/10.1007/s00026-006-0284-8
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DOI: https://doi.org/10.1007/s00026-006-0284-8
Keywords.
- unfolding model
- ranking pattern
- arrangement of hyperplanes
- characteristic polynomial
- mid-hyperplane arrangement
- spherical tetrahedron