کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4668092 1345496 2007 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Chambers of arrangements of hyperplanes and Arrow's impossibility theorem
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Chambers of arrangements of hyperplanes and Arrow's impossibility theorem
چکیده انگلیسی

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 by (if C⊆H+) and (if C⊆H−). Define . Let Chm=Ch×Ch×⋯×Ch (m times). Then the maps induce the maps . We will study the admissible maps which are compatible with every . 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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 214, Issue 1, 10 September 2007, Pages 366-378