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Showing 1 to 11 of 11 for “"Hyperplane arrangement"”.
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Monomization of power Ideals and parking functions
… are derived from a zonotope, or dually it's hyperplane arrangement. In the case that the hyperplane arrangement is of Type A, we can rephrase the definition in terms of graphs. Using the symmetry of these ideals, we can find monomial ideals which preserve much of the structure of the …
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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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Some problems in polynomial interpolation and topological complexity
… discuss the motion planning problem in complex hyperplane arrangement complements. The difficulty of constructing a minimally discontinuous motion planning algorithm for a topological space X is measured by an integer invariant of X called topological complexity or TC(X). Yuzvinsky developed a …
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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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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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Toric mirror symmetry and GIT windows
… over C^k stratified by a complexified periodic hyperplane arrangement whose complement models both parameter spaces. We obtain a universal deformation of skeletons interpolating variation of parameters."
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PROBABILISTIC MODELS FOR DEPENDENT VARIABLES: COMPLEX ANALYTIC AND COMBINATORIAL APPROACHES
… in probability theory and MAT-labeled graphs in hyperplane arrangement theory. We show that there exists an explicit equivalence between the categories of locally regular vines and MAT-labeled graphs. Several applications will be mentioned to illustrate the interaction between the two concepts. …
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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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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 …
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Homological properties of determinantal arrangements
<p>We study a certain family of hypersurface arrangements known as determinantal arrangements. Determinantal arrangements are a union of varieties defined by minors of a matrix of indeterminates. In particular, we investigate determinantal arrangements using the 2-minors of a 2 × <em>n</em> generic …
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Splines on polytopal complexes
… with the intersection lattice of a certain hyperplane arrangement. These build on work of Rose \cite{r1,r2} on dual graphs. It is well-known that the dimension of the vector space $C^r_d(\PC)$ agrees with a polynomial in $d$ for $d\gg 0$. In commutative algebra this polynomial is in fact the …