2023-04-01T17:44:28Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/696132022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Faces of arrangements of hyperplanes and Arrow's impossibility theoremAbe, Takuroopen access410In \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.Department of Mathematics, Hokkaido University2006-09-20engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83955http://hdl.handle.net/2115/6961310.14943/83955Hokkaido University Preprint Series in Mathematics805110https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69613/1/pre805.pdfapplication/pdf105.8 KB2006-09-20