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Faces of arrangements of hyperplanes and Arrow's impossibility theorem

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83955

Title: Faces of arrangements of hyperplanes and Arrow's impossibility theorem
Authors: Abe, Takuro Browse this author
Issue Date: 20-Sep-2006
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 805
Start Page: 1
End Page: 10
Abstract: In \cite{T}, Terao introduced an admissible map of chambers of a real central arrangement, and completely classified it. An admissible map is a generalization of a social welfare function and Terao's classification is that of Arrow's impossibility theorem in economics. In this article we consider an admissible map not of chambers but faces, and show that an admissible map of faces is a projection to a component if an arrangement is indecomposable and its cardinality is not less than three. From the view point of Arrow's theorem, our result corresponds to the impossibility theorem of a welfare function which permits the ''tie" choice.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69613
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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