Results 1 to 10 of about 304 (161)
The Varchenko determinant of a Coxeter arrangement [PDF]
Journal of Group Theory, 2018 AbstractThe Varchenko determinant is the determinant of a matrix defined from an arrangement of hyperplanes. Varchenko proved that this determinant has a beautiful factorization. It is, however, not possible to use this factorization to compute a Varchenko determinant from a certain level of complexity.
Gotz Pfeiffer, Hery Randriamaro
exaly +8 more sources
Deformations of Coxeter Hyperplane Arrangements
Journal of Combinatorial Theory - Series A, 2000 33 ...
Alexander Postnikov, Richard P Stanley
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Coxeter and crystallographic arrangements are inductively free
Advances in Mathematics, 2012 22 ...
Mohamed Barakat, Michael Cuntz
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Shi arrangements and low elements in Coxeter groups
Proceedings of the London Mathematical SocietyAbstractGiven an arbitrary Coxeter system and a non‐negative integer , the ‐Shi arrangement of is a subarrangement of the Coxeter hyperplane arrangement of . The classical Shi arrangement () was introduced in the case of affine Weyl groups by Shi to study Kazhdan–Lusztig cells for .
Dyer, Matthew +3 more
wiley +4 more sources
Coxeter arrangements in three dimensions [PDF]
Beitrage Zur Algebra Und Geometrie, 2016 6 pages, 1 ...
Richard Ehrenborg +2 more
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Counting chambers in restricted Coxeter arrangements
Archiv Der Mathematik, 2019 11 ...
Gerhard Röhrle, Röhrle Gerhard
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Periodic arrangements of tetrahedra having appearances similar to that of the Boerdijk–Coxeter helix [PDF]
Scientific ReportsThe Boerdijk-Coxeter helix (BC helix or tetrahelix) is a linear stacking of regular tetrahedra. Although the BC helix exhibits an aperiodic nature, structures resembling the BC helix with periodicity are found in materials. To understand such structures, we considered a modification of the BC helix to introduce periodicity.
Onaka S.
openaire +4 more sources
The primitive derivation and freeness of multi-Coxeter arrangements
Proceedings of the Japan Academy Series A: Mathematical Sciences, 2002 We will prove the freeness of multi-Coxeter arrangements by constructing a basis of the module of vector fields which contact to each reflecting hyperplanes with some multiplicities using K. Saito's theory of primitive derivation.
Masahiko Yoshinaga
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Modules of Differential Operators of Order 2 on Coxeter Arrangements [PDF]
Algebras and Representation Theory, 2013 We prove that the modules of differential operators of order 2 on the classical Coxeter arrangements are free by exhibiting bases. For this purpose, we use Cauchy-Sylvester's theorem on compound determinants and Saito-Holm's criterion. In the case type $A$, we apply Cauchy-Sylvester's theorem on compound determinants to Vandermond determinant. By using
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Conjectures for Cutting Pizza with Coxeter Arrangements
Experimental MathematicsWe are interested in conjecturing the sign of the pizza quantity P(H,B(a,R)) for the irreducible Coxeter arrangements H of type A_n, where n=2,3 bmod 4, and type D_n, where n is odd. Our approach is to express the pizza quantity in terms of the pizza quantity of subarrangements known as 2-structures, and we obtain the first non-zero term in the ...
Richard Ehrenborg
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