Advanced Studies in Pure Mathematics

Application of arrangement theory to unfolding models

Hidehiko Kamiya, Akimichi Takemura, and Norihide Tokushige

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Abstract

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.

Article information

Source
Arrangements of Hyperplanes — Sapporo 2009, H. Terao and S. Yuzvinsky, eds. (Tokyo: Mathematical Society of Japan, 2012), 399-415

Dates
Received: 25 March 2010
Revised: 6 August 2010
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543085016

Digital Object Identifier
doi:10.2969/aspm/06210399

Mathematical Reviews number (MathSciNet)
MR2933804

Zentralblatt MATH identifier
1256.32028

Subjects
Primary: 32S22: Relations with arrangements of hyperplanes [See also 52C35] 52C35: Arrangements of points, flats, hyperplanes [See also 32S22] 62F07: Ranking and selection

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

Citation

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


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