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Faces of arrangements of hyperplanes and Arrow's impossibility theorem
| Title: | Faces of arrangements of hyperplanes and Arrow's impossibility theorem |
| Authors: | Abe, Takuro Browse this author |
| Issue Date: | 20-Sep-2006 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
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Submitter: 数学紀要登録作業用
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