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Chambers of arrangements of hyperplanes and Arrow's impossibility theorem

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タイトル: Chambers of arrangements of hyperplanes and Arrow's impossibility theorem
著者: Terao, Hiroaki 著作を一覧する
キーワード: Arrangement of hyperplanes
Braid arrangements
Arrow's impossibility theorem
発行日: 2007年 9月10日
出版者: Elsevier Inc.
誌名: Advances in Mathematics
巻: 214
号: 1
開始ページ: 366
終了ページ: 378
出版社 DOI: 10.1016/j.aim.2007.02.006
抄録: Let A be a nonempty real central arrangement of hyperplanes and Ch be the set of chambers of A. Each hyperplane H defines a half-space H+ and the other half-space H−. Let B={+,−}. For H ∈ A, define a map ∈+H : Ch → B by ∈+H(C) = + (if C ⊆ H+) and ∈+H(C) = - (if C ⊆ H−). Define ∈-H = -∈+H. Let Chm=Ch×Ch×・・・×Ch (m times). Then the maps ∈±H induce the maps ∈±H : Chm → Bm. We will study the admissible maps Φ : Chm → Ch which are compatible with every ∈±H. Suppose |A| ≥ 3 and m ≥ 2. Then we will show that A is indecomposable if and only if every admissible map is a projection to a component. When A is a braid arrangement, which is indecomposable, this result is equivalent to Arrow's impossibility theorem in economics. We also determine the set of admissible maps explicitly for every nonempty real central arrangement.
資料タイプ: article (author version)
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 寺尾 宏明


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