Zobrazeno 1 - 10
of 18
pro vyhledávání: '"Torsten Hoge"'
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AT,..., Iss Proceedings (2014)
A Weyl arrangement is the arrangement defined by the root system of a finite Weyl group. When a set of positive roots is an ideal in the root poset, we call the corresponding arrangement an ideal subarrangement. Our main theorem asserts that any idea
Externí odkaz:
https://doaj.org/article/f0277c8030d84dfeb8609c049b18d8ee
Publikováno v:
Advances in Mathematics. 350:63-96
In 2002, Terao showed that every reflection multi-arrangement of a real reflection group with constant multiplicity is free by providing a basis of the module of derivations. We first generalize Terao's result to multi-arrangements stemming from well
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::88f0585ccacc8aed05cf4c68272fbd98
https://doi.org/10.1016/j.aim.2019.04.044
https://doi.org/10.1016/j.aim.2019.04.044
Autor:
Torsten Hoge, Gerhard Röhrle
Publikováno v:
Tohoku Mathematical Journal. 73
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::21ee584a22a371c7eb97144d60833fe6
https://doi.org/10.2748/tmj.20200318
https://doi.org/10.2748/tmj.20200318
Autor:
Torsten Hoge, Gerhard Röhrle
Publikováno v:
Journal of Algebra. 512:357-381
Let A be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction A ″ of A to any hyperplane endowed with the natural multiplicity is then a free multiarrangement. We initiate a study of the stronger freeness property of inductiv
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b8da3c0acbbf4722337dd821129a9ca5
https://doi.org/10.1016/j.jalgebra.2018.06.037
https://doi.org/10.1016/j.jalgebra.2018.06.037
Autor:
Gerhard Röhrle, Torsten Hoge
Publikováno v:
European Journal of Combinatorics. 55:20-40
We study the notion of a nice partition or factorization of a hyperplane arrangement due to Terao from the early 1990s. The principal aim of this note is an analogue of Terao's celebrated addition-deletion theorem for free arrangements for the class
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8e0194a54629946cf1938f23024ebe7d
https://doi.org/10.1016/j.ejc.2016.01.004
https://doi.org/10.1016/j.ejc.2016.01.004
Publikováno v:
Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory ISBN: 9783319705651
The class of free multiarrangements is known to be closed under taking localizations. We extend this result to the stronger notions of inductive and recursive freeness. As an application, we prove that recursively free (multi)arrangements are compati
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c452e317760ac78e4ed750b1524fb1e9
https://doi.org/10.1007/978-3-319-70566-8_16
https://doi.org/10.1007/978-3-319-70566-8_16
Publikováno v:
Journal of Algebra. 418:197-212
Let W be a finite complex reflection group acting on the complex vector space V and let A(W) = (A(W), V) be the associated reflection arrangement. In an earlier paper by the last two authros, we classified all inductively free reflection arrangements
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d09f24759e95527696ceef4a26b73c33
https://doi.org/10.1016/j.jalgebra.2014.06.036
https://doi.org/10.1016/j.jalgebra.2014.06.036
Autor:
Torsten Hoge, Gerhard Röhrle
Publikováno v:
Experimental Mathematics. 23:448-451
In 1989, Ziegler introduced the concept of a multiarrangement. One natural example is the reflection arrangement of a unitary reflection group with multiplicity given by the number of reflections associated with each hyperplane. For all but three irr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::300a88bb512fd9a1dfe8d6394c0e9d2b
https://doi.org/10.1080/10586458.2014.939787
https://doi.org/10.1080/10586458.2014.939787
Autor:
Michael Cuntz, Torsten Hoge
Publikováno v:
Proceedings of the American Mathematical Society. 143:35-40
We construct counterexamples to the conjecture that every free arrangement is recursively free in characteristic zero. The intersection lattice of our smallest example has a realization over a finite field which is recursively free, thus recursive fr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0e7217654e68299e2ba81308cac6ce2a
https://doi.org/10.1090/s0002-9939-2014-12263-5
https://doi.org/10.1090/s0002-9939-2014-12263-5
Autor:
Gerhard Röhrle, Torsten Hoge
Publikováno v:
Proceedings of the American Mathematical Society. 142:3787-3799
Let A = (A, V ) be a complex hyperplane arrangement and let L(A) denote its intersection lattice. The arrangement A is called supersolvable, provided its lattice L(A) is supersolvable, a notion due to Stanley [Sta72]. Jambu and Terao [JT84, Thm. 4.2]
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::29478b40373e91618b36aa46e5d12a11
https://doi.org/10.1090/s0002-9939-2014-12144-7
https://doi.org/10.1090/s0002-9939-2014-12144-7