Results 11 to 20 of about 285,691 (303)
Total positivity, Schubert positivity, and geometric Satake [PDF]
Journal of Algebra, 2016 Let G be a simple and simply-connected complex algebraic group, and let X \subset G^\vee be the centralizer subgroup of a principal nilpotent element. Ginzburg and Peterson independently related the ring of functions on X with the homology ring of the affine Grassmannian Gr_G.
Lam, Thomas, Rietsch, Konstanze
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Hyperdeterminantal Total Positivity [PDF]
Symmetry, Integrability and Geometry: Methods and ApplicationsFor a given positive integer $m$, the concept of <I>hyperdeterminantal total positivity</I> is defined for a kernel $K\colon {\mathbb R}^{2m} \to {\mathbb R}$, thereby generalizing the classical concept of total positivity. Extending the fundamental example, $K(x,y) = \exp(xy)$, $x, y \in \mathbb{R}$, of a classical totally positive kernel,
Johnson, Kenneth W. +1 more
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Total Positivity and Convexity Preservation [PDF]
Journal of Approximation Theory, 1999 In this paper the author introduces a concept of \(d\)-convexity of curves in the \(d\)-dimensional space and characterizes totally positive blending systems in terms of \(d\)-convexity. He shows that for certain systems total positivity and rational convexity preservation are equivalent.
Floater, Michael S.
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Positive Hankel Matrices, Eigenvalues and Total Positivity [PDF]
MathematicsFor positive Hankel matrices, an interval containing all eigenvalues is obtained. With a stronger condition, we also construct two sharper intervals for the eigenvalue localization. The total positivity of positive Hankel matrices is analyzed.
Juan Manuel Peña
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The total positivity interval [PDF]
Linear Algebra and its Applications, 2004 The authors consider the important descriptors: totally positive, and the related terms (totally nonnegative and oscillatory). They define the concept of the total positivity interval of such matrices. They seek concretely this interval and investigate some properties of this.
Gladwell, G.M.L., Ghanbari, K.
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Total positivity and dependence of order statistics [PDF]
, 2023 In this comprehensive study, we delve deeply into the concept of multivariate total positivity, defining it in accordance with a direction. We rigorously explore numerous salient properties, shedding light on the nuances that characterize this notion ...
Amo Artero, Enrique de +4 more
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Total positivity order and the normal distribution [PDF]
, 2006 International audienceUnlike the usual stochastic order, total positivity order is closed under conditioning. Here we provide a general formulation of the preservation properties of the order under conditioning; we study certain properties of the order ...
Marco Scarsini +3 more
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Combinatorics of Positroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Recently Postnikov gave a combinatorial description of the cells in a totally-nonnegative Grassmannian. These cells correspond to a special class of matroids called positroids.
Suho Oh
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Totally positive matrices and totally positive hypergraphs
Linear Algebra and its Applications, 2001 This paper characterizes (0,1)-matrices which are totally positive, that is, all their minors are totally positive. First the case of \(1\times 1\) and \(2\times 2\) minors is characterized in terms of interval hypergraphs and then the general case is characterized in terms of a chain of cliques \(C_i\), \(C_i\cap C_j = \emptyset \Leftrightarrow |i-j ...
Kubicki, Grzegorz +2 more
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On the Total Positivity and Accurate Computations of r-Bell Polynomial Bases
Axioms, 2023 A new class of matrices defined in terms of r-Stirling numbers is introduced. These r-Stirling matrices are totally positive and determine the linear transformation between monomial and r-Bell polynomial bases.
Esmeralda Mainar +2 more
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