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VOL. 62 | 2012 Application of arrangement theory to unfolding models
Hidehiko Kamiya, Akimichi Takemura, Norihide Tokushige

Editor(s) Hiroaki Terao, Sergey Yuzvinsky


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.


Published: 1 January 2012
First available in Project Euclid: 24 November 2018

zbMATH: 1256.32028
MathSciNet: MR2933804

Digital Object Identifier: 10.2969/aspm/06210399

Primary: 32S22 , 52C35 , 62F07

Keywords: All-subset arrangement , braid arrangement , chamber , characteristic polynomial , finite field method , hyperplane arrangement , intersection poset , mid-hyperplane arrangement , partition lattice , ranking pattern , unfolding model

Rights: Copyright © 2012 Mathematical Society of Japan


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