Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Arrangements of Hyperplanes — Sapporo 2009, H. Terao and S. Yuzvinsky, eds. (Tokyo: Mathematical Society of Japan, 2012), 399 - 415
Application of arrangement theory to unfolding models
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 counting (i) the number of admissible rankings in an unfolding model and (ii) the number of ranking patterns generated by unfolding models. The paper is mostly expository but also contains some new results such as simple upper and lower bounds for the number of ranking patterns in the unidimensional case.
Received: 25 March 2010
Revised: 6 August 2010
First available in Project Euclid: 24 November 2018
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All-subset arrangement braid arrangement chamber characteristic polynomial finite field method hyperplane arrangement intersection poset mid-hyperplane arrangement partition lattice ranking pattern unfolding model
Kamiya, Hidehiko; Takemura, Akimichi; Tokushige, Norihide. Application of arrangement theory to unfolding models. Arrangements of Hyperplanes — Sapporo 2009, 399--415, Mathematical Society of Japan, Tokyo, Japan, 2012. doi:10.2969/aspm/06210399. https://projecteuclid.org/euclid.aspm/1543085016