Divisionally free arrangements of hyperplanes
نویسندگان
چکیده
منابع مشابه
Inductively Factored Signed-graphic Arrangements of Hyperplanes
In 1994, Edelman and Reiner characterized free and supersolvable hyperplane arrangements in the restricted interval [An−1, Bn]. In this paper, we give a characterization of inductively factored arrangements in this interval, and show that the same characterization also describes factored arrangements in this interval. These results use the compact notation of signed graphs introduced by Zaslavsky.
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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 ǫ H : Ch → B by ǫ H (C) = + (if C ⊆ H) and ǫ H (C) = − (if C ⊆ H). Define ǫ H = −ǫ H . Let Ch = Ch×Ch× · · · ×Ch (m times). Then the maps ǫ H induce the maps ǫ H : Ch → B. We will study the adm...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2015
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-015-0615-7