Teses / dissertações sobre o tema "Hyperplanes arrangements"
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Charles, Balthazar. "Combinatorics and computations : Cartan matrices of monoids & minimal elements of Shi arrangements". Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASG063.
Texto completo da fonteThis thesis presents an investigation into two distinct combinatorial subjects: the effective computation of Cartan matrices in monoid representation theory and the exploration of properties of minimal elements in Shi arrangements of Coxeter groups. Although disparate, both of these research focuses share a commonality in the utilization of combinatorial methods and computer exploration either as an end in itself for the former or as a help to research for the latter. In the first part of the dissertation, we develop methods for the effective computation of character tables and Cartan matrices in monoid representation theory. To this end, we present an algorithm based on our results for the efficient computations of fixed points under a conjugacy-like action, with the goal to implement Thiéry's formula for the Cartan matrix from [Thiéry '12]. After a largely self-contained introduction to the necessary background, we present our results for fixed-point counting, as well as a new formula for the character table of finite monoids. We evaluate the performance of the resulting algorithms in terms of execution time and memory usage and find that they are more efficient than algorithms not specialized for monoids by orders of magnitude. We hope that the resulting (public) implementation will contribute to the monoid representation community by allowing previously impractical computations. The second part of the thesis focuses on the properties of minimal elements in Shi arrangements. The Shi arrangements were introduced in [Shi '87] and are the object of Conjecture 2 from [Dyer, Hohlweg '14]. Originally motivated by this conjecture, we present two results. Firstly, a direct proof in the case of rank 3 groups. Secondly, in the special case of Weyl groups, we give a description of the minimal elements of the Shi regions by extending a bijection from [Athanasiadis, Linusson '99] and [Armstrong, Reiner, Rhoades '15] between parking functions and Shi regions. This allows for the effective computation of the minimal elements. From the properties of this computation, we provide a type-free proof of the conjecture in Weyl groups as an application. These results reveal an intriguing interplay between the non-nesting and non-crossing worlds in the case of classical Weyl groups
Johnston, David. "Quasi-invariants of hyperplane arrangements". Thesis, University of Glasgow, 2012. http://theses.gla.ac.uk/3169/.
Texto completo da fonteZiegler, Günter M. (Günter Matthias). "Algebraic combinatorics of hyperplane arrangements". Thesis, Massachusetts Institute of Technology, 1987. http://hdl.handle.net/1721.1/14854.
Texto completo da fonteMoseley, Daniel, e Daniel Moseley. "Group Actions on Hyperplane Arrangements". Thesis, University of Oregon, 2012. http://hdl.handle.net/1794/12373.
Texto completo da fonteBibby, Christin. "Abelian Arrangements". Thesis, University of Oregon, 2015. http://hdl.handle.net/1794/19273.
Texto completo da fonteSleumer, Nora Helena. "Hyperplane arrangements : construction, visualization and applications /". [S.l.] : [s.n.], 2000. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=13502.
Texto completo da fonteAgosti, Claudia. "Cohomology of hyperplane and toric arrangements". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19510/.
Texto completo da fonteMücksch, Paul [Verfasser]. "Combinatorics and freeness of hyperplane arrangements and reflection arrangements / Paul Mücksch". Hannover : Technische Informationsbibliothek (TIB), 2018. http://d-nb.info/1169961169/34.
Texto completo da fonteBiyikoglu, Türker, Wim Hordijk, Josef Leydold, Tomaz Pisanski e Peter F. Stadler. "Graph Laplacians, Nodal Domains, and Hyperplane Arrangements". Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, 2002. http://epub.wu.ac.at/1036/1/document.pdf.
Texto completo da fonteSeries: Preprint Series / Department of Applied Statistics and Data Processing
Moss, Aaron. "Basis Enumeration of Hyperplane Arrangements up to Symmetries". Thesis, Fredericton: University of New Brunswick, 2012. http://hdl.handle.net/1882/44593.
Texto completo da fonteHager, Amanda C. "Freeness of hyperplane arrangement bundles and local homology of arrangement complements". Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/678.
Texto completo da fonteWilliams, Kristopher John. "The Milnor fiber associated to an arrangement of hyperplanes". Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1277.
Texto completo da fonteArdila, Federico 1977. "Enumerative and algebraic aspects of matroids and hyperplane arrangements". Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/29287.
Texto completo da fonteIncludes bibliographical references (p. 109-115).
This thesis consists of three projects on the enumerative and algebraic properties of matroids and hyperplane arrangements. In particular, a central object of study is the Tutte polynomial, which stores much of the enumerative information of these objects. The first project is the study of the Tutte polynomial of an arrangement and, more generally, of a semimatroid. It has two components: an enumerative one and a matroid-theoretic one. We start by considering purely enumerative questions about the Tutte polynomial of a hyperplane arrangement. We introduce a new method for computing it, which generalizes several known results. We apply our method to several specific arrangements, thus relating the computation of Tutte polynomials to problems in enumerative combinatorics. As a consequence, we obtain several new results about classical combinatorial objects such as labeled trees, Dyck paths, semiorders and alternating trees. We then address matroid-theoretic aspects of arrangements and their Tutte polynomials. We start by defining semimatroids, a class of objects which abstracts the dependence properties of an affine hyperplane arrangement. After discussing these objects in detail, we define and investigate their Tutte polynomial. In particular, we prove that it is the universal Tutte-Grothendieck invariant for semimatroids, and we give a combinatorial interpretation for its non-negative coefficients. The second project is the beginning of an attempt to study the Tutte polynomial from an algebraic point of view.
(cont.) Given a matroid representable over a field of characteristic zero, we construct a graded algebra whose Hilbert-Poincar6 series is a simple evaluation of the Tutte polynomial of the matroid. This construction is joint work with Alex Postnikov. The third project involves a class of matroids with very rich enumerative properties. We show how the set of Dyck paths of length 2n naturally gives rise to a matroid, which we call the Catalan matroid Cn. We describe this matroid in detail; among several other results, we show that Cn is self-dual, it is representable over the rationals but not over finite fields Fq with q < n - 2, and it has a nice Tutte polynomial. We then introduce a more general family of matroids, which we call shifted matroids. They are precisely the matroids whose independence complex is a shifted simplicial complex.
by Federico Ardila.
Ph.D.
Tohaneanu, Stefan Ovidiu. "Homological algebra and problems in combinatorics and geometry". Texas A&M University, 2003. http://hdl.handle.net/1969.1/5789.
Texto completo da fonteWakefield, Max. "On the derivation module and apolar algebra of an arrangement of hyperplanes /". view abstract or download file of text, 2006. http://proquest.umi.com/pqdweb?did=1188874511&sid=1&Fmt=2&clientId=11238&RQT=309&VName=PQD.
Texto completo da fonteTypescript. Includes vita and abstract. Includes bibliographical references (leaves 83-84). Also available for download via the World Wide Web; free to University of Oregon users.
Kebede, Sebsibew. "On Bernstein-Sato ideals and Decomposition of D-modules over Hyperplane Arrangements". Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-129493.
Texto completo da fonteZhang, Yang. "Combinatorics of Milnor fibres of reflection arrangements". Thesis, University of Sydney, 2020. https://hdl.handle.net/2123/22985.
Texto completo da fontePaolini, Giovanni. "Topology and combinatorics of affine reflection arrangements". Doctoral thesis, Scuola Normale Superiore, 2019. http://hdl.handle.net/11384/85743.
Texto completo da fonteBailet, Pauline. "Arrangements d'hyperplans". Phd thesis, Université Nice Sophia Antipolis, 2014. http://tel.archives-ouvertes.fr/tel-01059809.
Texto completo da fonteMöller, Tilman Hendrik [Verfasser], Gerhard [Gutachter] Röhrle, Christian [Gutachter] Stump e Graham [Gutachter] Denham. "Combinatorial properties of hyperplane arrangements and reflection arrangements / Tilman Hendrik Möller ; Gutachter: Gerhard Röhrle, Christian Stump, Graham Denham ; Fakultät für Mathematik". Bochum : Ruhr-Universität Bochum, 2019. http://d-nb.info/1185171819/34.
Texto completo da fonteMöller, Tilman [Verfasser], Gerhard [Gutachter] Röhrle, Christian [Gutachter] Stump e Graham [Gutachter] Denham. "Combinatorial properties of hyperplane arrangements and reflection arrangements / Tilman Hendrik Möller ; Gutachter: Gerhard Röhrle, Christian Stump, Graham Denham ; Fakultät für Mathematik". Bochum : Ruhr-Universität Bochum, 2019. http://d-nb.info/1185171819/34.
Texto completo da fonteBartz, Jeremiah. "Multinets in P^2 and P^3". Thesis, University of Oregon, 2013. http://hdl.handle.net/1794/13252.
Texto completo da fonteLund, Benjamin. "Some Results in Discrete Geometry". University of Cincinnati / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1342463167.
Texto completo da fonteVo, Phi Khanh. "Contributions à l'étude des arrangements : équivalences combinatoires et perturbations". Université Joseph Fourier (Grenoble), 1994. http://tel.archives-ouvertes.fr/tel-00344973.
Texto completo da fonteRattan, Amarpreet. "Parking Functions and Related Combinatorial Structures". Thesis, University of Waterloo, 2001. http://hdl.handle.net/10012/1028.
Texto completo da fonteVenturelli, Federico. "The Alexander polynomial of certain classes of non-symmetric line arrangements". Doctoral thesis, Università degli studi di Padova, 2019. http://hdl.handle.net/11577/3422691.
Texto completo da fonteDupont, Clément. "Périodes des arrangements d'hyperplans et coproduit motivique". Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066207.
Texto completo da fonteIn this thesis, we deal with some questions about hyperplane arrangements from the viewpoint of motivic periods. Following a program initiated by Beilinson et al., we study a family of periods called Aomoto polylogarithms and their motivic variants, viewed as elements of the fundamental Hopf algebra of the category of mixed Hodge-Tate structures, or the category of mixed Tate motives over a number field. We start by computing the motivic coproduct of a family of such periods, called generic dissection polylogarithms, showing that it is governed by a combinatorial formula. This result generalizes a theorem of Goncharov on iterated integrals. Then, we introduce bi-arrangements of hyperplanes, which are geometric and combinatorial objects which generalize classical hyperplane arrangements. The computation of relative cohomology groups associated to bi-arrangements of hyperplanes is a crucial step in the understanding of the motivic coproduct of Aomoto polylogarithms. We define cohomological and combinatorial tools to compute these cohomology groups, which recast classical objects such as the Orlik-Solomon algebra in a global setting
Le, Giang T. "The Action Dimension of Artin Groups". The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1469011775.
Texto completo da fonteRada, Miroslav. "Algoritmy pro vybrané geometrické problémy nad zonotopy a jejich aplikace v optimalizaci a v analýze dat". Doctoral thesis, Vysoká škola ekonomická v Praze, 2009. http://www.nusl.cz/ntk/nusl-199386.
Texto completo da fonteShokrieh, Farbod. "Divisors on graphs, binomial and monomial ideals, and cellular resolutions". Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/52176.
Texto completo da fonteRousset, Mireille. "Sommes de Minkowski de triangles". Phd thesis, Université Joseph Fourier (Grenoble), 1996. http://tel.archives-ouvertes.fr/tel-00005017.
Texto completo da fonte"Graph Laplacians, Nodal Domains, and Hyperplane Arrangements". Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, 2002. http://epub.wu-wien.ac.at/dyn/dl/wp/epub-wu-01_9f2.
Texto completo da fonteGeldon, Todd Wolman. "Computing the Tutte Polynomial of hyperplane arrangements". 2009. http://hdl.handle.net/2152/6660.
Texto completo da fontetext
Biyikoglu, Türker, Wim Hordijk, Josef Leydold, Tomaz Pisanski e Peter F. Stadler. "Graph Laplacians, Nodal Domains, and Hyperplane Arrangements". 2004. https://ul.qucosa.de/id/qucosa%3A32145.
Texto completo da fonteArvola, William Arthur. "The fundamental group of the complement of an arrangement of complex hyperplanes". 1991. http://catalog.hathitrust.org/api/volumes/oclc/24492863.html.
Texto completo da fonteTypescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 67).
Thieu, Dinh Phong. "On graded ideals over the exterior algebra with applications to hyperplane arrangements". Doctoral thesis, 2013. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2013092311626.
Texto completo da fonteBrandt, Keith Allan. "A combinatorial study of the module of derivations of an arrangement of hyperplanes". 1992. http://catalog.hathitrust.org/api/volumes/oclc/28726852.html.
Texto completo da fonteTypescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 86-87).
Le, Van Dinh. "The broken circuit complex and the Orlik - Terao algebra of a hyperplane arrangement". Doctoral thesis, 2016. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2016021714257.
Texto completo da fonteVo, Phi Khanh. "Contributions à l'étude des arrangements: Equivalences combinatoires et perturbations". Phd thesis, 1994. http://tel.archives-ouvertes.fr/tel-00344973.
Texto completo da fonteNarkawicz, Anthony Joseph. "Cohomology Jumping Loci and the Relative Malcev Completion". Diss., 2007. http://hdl.handle.net/10161/441.
Texto completo da fonte(10724076), Daniel L. Bath. "Bernstein--Sato Ideals and the Logarithmic Data of a Divisor". Thesis, 2021.
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