Coxeter and crystallographic arrangements are inductively free
Copyright policy )Coxeter and crystallographic arrangements are inductively free
Using the classification of finite Weyl groupoids we prove that crystallographic arrangements, a large subclass of the class of simplicial arrangements which was recently defined, are hereditarily inductively free. In particular, all crystallographic reflection arrangements are hereditarily inductively free, among them the arrangement of type $E_8$. With little extra work we prove that also all Coxeter arrangements are inductively free.
22 pages
Mathematics(all), arrangement of hyperplanes, Coxeter arrangements, Reflection, Inductively free, inductively free, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), crystallographic reflection arrangements, 20F55, 52C35, 05E45, crystallographic arrangements, Mathematics - Quantum Algebra, Coxeter, FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), Arrangement of hyperplanes
Mathematics(all), arrangement of hyperplanes, Coxeter arrangements, Reflection, Inductively free, inductively free, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), crystallographic reflection arrangements, 20F55, 52C35, 05E45, crystallographic arrangements, Mathematics - Quantum Algebra, Coxeter, FOS: Mathematics, Mathematics - Combinatorics, Quantum Algebra (math.QA), Combinatorics (math.CO), Arrangement of hyperplanes
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