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Total positivity for cominuscule Grassmannians [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 In this paper we explore the combinatorics of the non-negative part $(G/P)_{\geq 0}$ of a cominuscule Grassmannian. For each such Grassmannian we define Le-diagrams ― certain fillings of generalized Young diagrams which are in bijection with the cells of
Thomas Lam, Lauren Williams
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Total positivity for the Lagrangian Grassmannian [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The positroid decomposition of the Grassmannian refines the well-known Schubert decomposition, and has a rich combinatorial structure. There are a number of interesting combinatorial posets which index positroid varieties,just as Young diagrams index ...
Rachel Karpman
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On stochastic orders and total positivity
ESAIM: Probability and Statistics, 2023 The usual stochastic order and the likelihood ratio order between probability distributions on the real line are reviewed in full generality. In addition, for the distribution of a random pair (X, Y), it is shown that the conditional distributions of Y, given X = x, are increasing in x with respect to the likelihood ratio order if and only if the joint
Lutz Dümbgen, Alexandre Mösching
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Reliability Properties of the NDL Family of Discrete Distributions with Its Inference
Mathematics, 2021 The natural discrete Lindley (NDL) distribution is an intuitive idea that uses discrete analogs to well-known continuous distributions rather than using any of the published discretization techniques. The NDL is a flexible extension of both the geometric
Mohammed Mohammed Ahmed Almazah +3 more
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Green Matrices, Minors and Hadamard Products
Axioms, 2023 Green matrices are interpreted as discrete version of Green functions and are used when working with inhomogeneous linear system of differential equations.
Jorge Delgado +2 more
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On Plücker coordinates of a perfectly oriented planar network [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Let $G$ be a perfectly oriented planar graph. Postnikov's boundary measurement construction provides a rational map from the set of positive weight functions on the edges of $G$ onto the appropriate totally nonnegative Grassmann cell.
Kelli Talaska
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Total Positivity: Tests and Parametrizations [PDF]
The Mathematical Intelligencer, 2000 An introduction to total positivity (TP), with the emphasis on efficient TP criteria and parametrizations of TP matrices. Intended for general mathematical audience.
Fomin, Sergey, Zelevinsky, Andrei
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Sign variation, the Grassmannian, and total positivity [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The totally nonnegative Grassmannian is the set of $k$-dimensional subspaces $V$ of ℝ$n$ whose nonzero Plücker coordinates (i.e. $k × k$ minors of a $k × n$ matrix whose rows span $V$) all have the same sign.
Steven N. Karp
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The Tropical Totally Positive Grassmannian [PDF]
Journal of Algebraic Combinatorics, 2005 Tropical algebraic geometry is the geometry of the tropical semiring (R, min, +). The theory of total positivity is a natural generalization of the study of matrices with all minors positive. In this paper we introduce the totally positive part of the tropicalization of an arbitrary affine variety, an object which has the structure of a polyhedral fan.
Speyer, David, Williams, Lauren
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A Generalized Quasi Cubic Trigonometric Bernstein Basis Functions and Its B-Spline Form
Mathematics, 2021 In this paper, under the framework of Extended Chebyshev space, four new generalized quasi cubic trigonometric Bernstein basis functions with two shape functions α(t) and β(t) are constructed in a generalized quasi cubic trigonometric space span{1,sin2t,(
Yunyi Fu, Yuanpeng Zhu
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