# Ranking patterns of unfolding models of codimension one

@article{Kamiya2011RankingPO, title={Ranking patterns of unfolding models of codimension one}, author={Hidehiko Kamiya and Akimichi Takemura and Hiroaki Terao}, journal={Adv. Appl. Math.}, year={2011}, volume={47}, pages={379-400} }

We consider the problem of counting the number of possible sets of rankings (called ranking patterns) generated by unfolding models of codimension one. We express the ranking patterns as slices of the braid arrangement and show that all braid slices, including those not associated with unfolding models, are in one-to-one correspondence with the chambers of an arrangement. By identifying those which are associated with unfolding models, we find the number of ranking patterns. We also give an…

## 21 Citations

Application of arrangement theory to unfolding models

- Mathematics
- 2010

Arrangement theory plays an essential role in the study of the unfolding model used in many fields. This paper describes how arrangement theory can be usefully employed in solving the problems of…

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Application of Arrangement Theory to Unfolding Models

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This paper describes how arrangement theory can be usefully employed in solving the problems of counting (i) the number of admissible rankings in an unfolding model and (ii) theNumber of ranking patterns generated by unfolding models.

Maximal unbalanced families

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- Mathematics, Computer ScienceElectron. J. Comb.
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- 2012

Let B be a real hyperplane arrangement which is stable under the action of a Coxeter group W. Then W acts naturally on the set of chambers of B. We assume that B is disjoint from the Coxeter…

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