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Showing 1 to 12 of 12 for “"Hyperplane arrangements"”.
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Species and Hyperplane Arrangements
… of species and the Tits algebra of a real hyperplane arrangement. The relation between these two comes from the work of Aguiar and Mahajan (2013), who showed that a (co)commutative Hopf monoid gives rise to a family of (left)right-modules over the Tits algebra of the braid arrangement in …
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Algebraic combinatorics of hyperplane arrangements
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1987.
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Enumerative and algebraic aspects of matroids and hyperplane arrangements
… 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 …
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Symmetric structures in the weak and strong Bruhat orders
… connections to Schubert calculus, Lie algebras, hyperplane arrangements, sorting networks and so on. In this thesis, we study various new symmetries within these structures, including the balance constant and the hull metric property of the weak order, and the self-dual intervals and boolean …
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Lattice Subdivisions and Tropical Oriented Matroids, Featuring Products of Simplices
… questions. Chapter two discusses tropical hyperplane arrangements and the tropical oriented matroid theory they inspire, paying particular attention to the previously uninvestigated distinction between the generic and non-generic cases. The focus of chapter three is products of simplices, …
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Ad-nilpotent ideals of complex and real reductive groups
… orbits, affine Weyl groups, sign types and hyperplane arrangements. This thesis is divided into three parts. The first and second parts deal with ad-nilpotent ideals for complex reductive Lie groups. In the first part, we study the left equivalence relation of ad-nilpotent ideals and relate …
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Essays in Computational Econometrics
… algorithm for enumerating the cells induced by hyperplane arrangements. The third essay examines the problem of inference on the value function of a linear program where the right-hand side parameters are random. A tractable method for developing confidence intervals is presented that has …
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Combinatorics in Schubert varieties and Specht modules
… Schubert varieties in the full flag variety with hyperplane arrangements. Schubert varieties are parameterized by elements of the Weyl group. For each element of the Weyl group, we construct certain hyperplane arrangement. We show that the generating function for regions of this arrangement …
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Double affine galleries
… develop a theory of galleries for double affine hyperplane arrangements. A gallery is an infinite sequence of chambers, indexed by an ordered set, which is maximal with respect to a finiteness condition on the multiset of wall-crossings. We study the possible order types of galleries. We also use …
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Combinatorics of acyclic orientations of graphs : algebra, geometry and probability
… combinatorics, and of the geometry of hyperplane arrangements and zonotopes. What can be said about the distribution of acyclic orientations obtained from a uniformly random selection of bijective labelling? What orientations are thence more probable? What can be said about the case of …
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Root system chip-firing
… These are analogous to the Catalan and Shi hyperplane arrangements. We prove that these interval-firing processes are always confluent from all initial weights. In Chapter 5 we study the set of weights with given interval-firing stabilization. We show that the number of weights with given …
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Cohomology Jumping Loci and the Relative Malcev Completion
… the fundamental group of the complement X of a hyperplane arrangement are the Malcev completion of its fundamental group G and the cohomology groups of X with coefficients in rank one local systems. In this thesis, we develop a tool that unifies these two approaches. This tool is the Malcev …