Results 11 to 20 of about 58 (47)
Supersolvable restrictions of reflection arrangements
Journal of Combinatorial Theory - Series A, 2014 16 pages; final version, to appear in Journal of Combinatorial Theory, Series ...
Gerhard Roehrle, Torsten Hoge
exaly +4 more sources
Supersolvable resolutions of line arrangements
Hokkaido Mathematical Journal, 2023 9 pages, 1 ...
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On the geometry of real or complex supersolvable line arrangements
Journal of Combinatorial Theory - Series A, 2016 Given a rank 3 real arrangement $\mathcal A$ of $n$ lines in the projective plane, the Dirac-Motzkin conjecture (proved by Green and Tao in 2013) states that for $n$ sufficiently large, the number of simple intersection points of $\mathcal A$ is greater than or equal to $n/2$.
Stefan O Tohaneanu
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The Counting Polynomial of a Supersolvable Arrangement
Advances in Mathematics, 1995 Let \(A\) be an arrangement of hyperplanes in a real finite dimensional vector space \(V\). The components of the complement of the union of the hyperplanes are called the chambers of \(A\). The counting polynomial \(\sum_{i \geq 0} a_i t^i\) of \(A\) in a chamber \(C\) is defined by setting \(a_i\) equal to the number of chambers which are separated ...
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On complex supersolvable line arrangements
Journal of Algebra, 2020 v.9: Takuro Abe joins as a co-author, after proving that the conjectural upper bounds 3m-3 holds indeed.
Alexandru Dimca, Takuro Abe
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Worpitzky-compatible subarrangements of braid arrangements and cocomparability graphs
Comptes Rendus. Mathématique, 2021 The class of Worpitzky-compatible subarrangements of a Weyl arrangement together with an associated Eulerian polynomial was recently introduced by Ashraf, Yoshinaga and the first author, which brings the characteristic and Ehrhart quasi-polynomials into ...
Tran, Tan Nhat, Tsuchiya, Akiyoshi
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Supersolvable reflection arrangements [PDF]
Proceedings of the American Mathematical Society, 2014 Let A = ( A
Hoge, Torsten, Röhrle, Gerhard
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Graded Linearity of Stanley–Reisner Ring of Broken Circuit Complexes
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 This paper introduces two new notions of graded linear resolution and graded linear quotients, which generalize the concepts of linear resolution property and linear quotient for modules over the polynomial ring A = k[x1, …, xn]. Besides, we compare graded linearity with componentwise linearity in general.
Mohammad Reza-Rahmati +2 more
wiley +1 more source
Supersolvable simplicial arrangements [PDF]
Advances in Applied Mathematics, 2019 Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane arrangements with particularly nice geometric, algebraic, topological, and combinatorial properties are the ...
Michael Cuntz, Paul Mücksch
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The freeness of Ish arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The Ish arrangement was introduced by Armstrong to give a new interpretation of the $q; t$-Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some striking similarities between the Shi arrangement and the Ish arrangement ...
Takuro Abe +2 more
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