Apoorva Khare

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All published works

Action	Title	Year	Authors
+ PDF Chat	Numerical radius and $\ell_p$ operator norm of Kronecker products: inequalities and equalities	2025	Pintu Bhunia Sujit Sakharam Damase Apoorva Khare
+ PDF Chat	Multivariate transforms of total positivity	2024	Sujit Sakharam Damase Apoorva Khare
+	Probability inequalities for strongly left-invariant metric semigroups/monoids, including all lie groups	2024	Apoorva Khare
+	KRP’s contributions in Lie theory	2024	Apoorva Khare
+ PDF	The blowup-polynomial of a metric space: connections to stable polynomials, graphs and their distance spectra	2023	Projesh Nath Choudhury Apoorva Khare
+	Distance matrices of a tree: Two more invariants, and in a unified framework	2023	Projesh Nath Choudhury Apoorva Khare
+ PDF	The Khinchin–Kahane and Lévy inequalities for abelian metric groups, and transfer from normed (abelian semi)groups to Banach spaces	2023	Apoorva Khare Bala Rajaratnam
+ PDF Chat	Recovering affine linearity of functions from their restrictions to affine lines	2023	Apoorva Khare Akaki Tikaradze
+ PDF	Totally positive kernels, Pólya frequency functions, and their transforms	2023	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+ PDF	From Cauchy’s determinant formula to bosonic and fermionic immanant identities	2023	Apoorva Khare Siddhartha Sahi
+	Probability inequalities for strongly left-invariant metric semigroups/monoids, including all Lie groups	2023	Apoorva Khare
+	The additive-multiplicative distance matrix of a graph, and a novel third invariant	2023	Projesh Nath Choudhury Apoorva Khare
+	Negativity-preserving transforms of tuples of symmetric matrices	2023	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+	Matrix positivity preservers in fixed dimension. II: positive definiteness and strict monotonicity of Schur function ratios	2023	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+	A remark on characterizing inner product spaces via strong three-point homogeneity	2023	Sujit Sakharam Damase Apoorva Khare
+ PDF	Matrix compression along isogenic blocks	2022	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+ PDF	Preservers of totally positive kernels and Pólya frequency functions	2022	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+ PDF Chat	Hirschman–Widder densities	2022	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+ PDF	The weights of simple modules in Category <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="script">O</mml:mi></mml:math> for Kac–Moody algebras	2022	Gurbir Dhillon Apoorva Khare
+	First-Order Approximation and the Leading Term of Schur Polynomials	2022	Apoorva Khare
+	Entrywise Functions Preserving Positivity in all Dimensions	2022	Apoorva Khare
+	Exact Quantitative Bound – Monotonicity of Schur Ratios	2022	Apoorva Khare
+	Polynomial Preservers for Rank-1 Matrices, via Schur Polynomials	2022	Apoorva Khare
+	Menger’s Results and Euclidean Distance Geometry	2022	Apoorva Khare
+	The Schur Product Theorem and Nonzero Lower Bounds	2022	Apoorva Khare
+	Preservers of Loewner Positivity on Kernels	2022	Apoorva Khare
+	Midconvex Implies Continuity, and 2 × 2 Preservers	2022	Apoorva Khare
+	The Cone of Positive Semidefinite Matrices	2022	Apoorva Khare
+	Functions Acting Outside Forbidden Diagonal Blocks	2022	Apoorva Khare
+	Totally Positive Matrices – Generalized Vandermonde and Hankel Moment Matrices	2022	Apoorva Khare
+	Entrywise Preservers of Positivity on Matrices with Zero Patterns	2022	Apoorva Khare
+	Preliminaries: Entrywise Powers Preserving Positivity in a Fixed Dimension	2022	Apoorva Khare
+	Proof of the Stronger Schoenberg Theorem (Part III) – Complex Analysis	2022	Apoorva Khare
+	Cauchy and Littlewood’s Definitions of Schur Polynomials	2022	Apoorva Khare
+	The Boas–Widder Theorem on Functions with Positive Differences	2022	Apoorva Khare
+	Entrywise Polynomial Preservers and Horn–Loewner-Type Conditions	2022	Apoorva Khare
+	Entrywise Powers Preserving Positivity in a Fixed Dimension	2022	Apoorva Khare
+	Loewner Convexity and Single Matrix Encoders of Preservers	2022	Apoorva Khare
+	The Stronger Horn–Loewner Theorem via Mollifiers	2022	Apoorva Khare
+	Polynomial Preservers on Matrices with Real or Complex Entries	2022	Apoorva Khare
+	Preservers of Loewner Monotonicity and Convexity on Kernels	2022	Apoorva Khare
+	Totally Positive (TP) and Totally Nonnegative (TN) Matrices	2022	Apoorva Khare
+	Entrywise Polynomials Preserving Positivity in a Fixed Dimension	2022	Apoorva Khare
+	A weight-formula for all highest weight modules, and a higher order parabolic category $\mathcal{O}$	2022	Apoorva Khare G. Krishna Teja
+	From Cauchy's determinant formula to bosonic and fermionic immanant identities	2022	Apoorva Khare Siddhartha Sahi
+	Blowup polynomials and delta-matroids of graphs	2022	Projesh Nath Choudhury Apoorva Khare
+	Recovering affine-linearity of functions from their restrictions to affine lines	2022	Apoorva Khare Akaki Tikaradze
+	The lattice of nil-Hecke algebras over a Coxeter group	2021	Sutanay Bhattacharya Apoorva Khare
+ PDF Chat	The lattice of nil-Hecke algebras over a Coxeter group	2021	Sutanay Bhattacharya Apoorva Khare
+	Preservers of totally positive kernels and Polya frequency functions	2021	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+ PDF Chat	The <i>p</i>-norm of circulant matrices	2021	Ludovick Bouthat Apoorva Khare Javad Mashreghi Frédéric Morneau-Guérin
+	Smooth entrywise positivity preservers, a Horn–Loewner master theorem, and symmetric function identities	2021	Apoorva Khare
+	The $p$-norm of circulant matrices	2021	Ludovick Bouthat Apoorva Khare Javad Mashreghi Frédéric Morneau-Guérin
+	Moment-sequence transforms	2021	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+ PDF Chat	Covering modules by proper submodules	2021	Apoorva Khare Akaki Tikaradze
+	Multivariate blowup-polynomials of graphs	2021	Projesh Nath Choudhury Apoorva Khare
+	Sharp nonzero lower bounds for the Schur product theorem	2021	Apoorva Khare
+ PDF Chat	Sign non‐reversal property for totally non‐negative and totally positive matrices, and testing total positivity of their interval hull	2021	Projesh Nath Choudhury M. Rajesh Kannan Apoorva Khare
+ PDF Chat	On an asymptotic characterisation of Griffiths semipositivity	2021	Apoorva Khare Vamsi Pritham Pingali
+ PDF Chat	On the sign patterns of entrywise positivity preservers in fixed dimension	2021	Apoorva Khare Terence Tao
+	Multivariate blowup-polynomials of graphs	2021	Projesh Nath Choudhury Apoorva Khare
+	The blowup-polynomial of a metric space: connections to stable polynomials, graphs and their distance spectra	2021	Projesh Nath Choudhury Apoorva Khare
+	The lattice of nil-Hecke algebras over real and complex reflection groups	2021	Sutanay Bhattacharya Apoorva Khare
+	12. Modular arithmetic I:Around the clock and the calendar	2020	Apoorva Khare Anna Lachowska
+	1. Algebra: The art and craft of computation	2020	Apoorva Khare Anna Lachowska
+	14. Probability: Dice, coins, cards, and winning streaks	2020	Apoorva Khare Anna Lachowska
+	13. Modular arithmetic II: How to keep (and break) secrets	2020	Apoorva Khare Anna Lachowska
+ PDF Chat	Differential calculus on the space of countable labelled graphs	2020	Apoorva Khare Bala Rajaratnam
+	Critical exponents for total positivity, individual kernel encoders, and the Jain-Karlin-Schoenberg kernel.	2020	Apoorva Khare
+	Post-composition transforms of totally positive kernels	2020	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+ PDF	Schur polynomials and matrix positivity preservers	2020	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+	Beautiful, Simple, Exact, Crazy	2020	Apoorva Khare Anna Lachowska
+ PDF Chat	Probability inequalities and tail estimates for metric semigroups	2020	Apoorva Khare Bala Rajaratnam
+	Multiply positive functions, critical exponent phenomena, and the Jain-Karlin-Schoenberg kernel	2020	Apoorva Khare
+	Matrix compression along isogenic blocks	2020	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+	Totally positive kernels, Polya frequency functions, and their transforms	2020	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+	Sharp uniform lower bounds for the Schur product theorem.	2019	Apoorva Khare
+ PDF	Hopf Algebras, Quantum Groups and Yang-Baxter Equations	2019	Florin F. Nichita Tomasz Brzezi Simon A. Fairfax Michiel Hazewinkel Jacob Laan Alexander E. Hoffnung K. Kanakoglou Apoorva Khare Joel Lemay Jon Links
+ PDF Chat	A Panorama of Positivity. I: Dimension Free	2019	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+	Distance matrices of a tree: two more invariants, and in a unified framework	2019	Projesh Nath Choudhury Apoorva Khare
+	A combinatorial model for computing volumes of flow polytopes	2018	Carolina Benedetti Rafael González S. D'León Christopher R. H. Hanusa Pamela E. Harris Apoorva Khare Alejandro H. Morales Martha Yip
+ PDF	Homogeneous length functions on groups	2018	T. A. Fritz Siddhartha Gadgil Apoorva Khare Pace P. Nielsen Lior Silberman Terence Tao
+	The normed space of norms on a finite-dimensional Banach space	2018	Apoorva Khare
+	The normed space of norms on Euclidean space	2018	Apoorva Khare
+	Smooth entrywise positivity preservers, a Horn-Loewner master theorem, and Schur polynomial identities	2018	Apoorva Khare
+	Smooth entrywise positivity preservers, a Horn-Loewner master theorem, and Schur polynomials	2018	Apoorva Khare
+	A Carlitz–von Staudt type theorem for finite rings	2018	Apoorva Khare Akaki Tikaradze
+	Simultaneous kernels of matrix Hadamard powers	2018	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+	Generalized nil-Coxeter algebras	2018	Apoorva Khare
+	The critical exponent: a novel graph invariant	2018	Dominique Guillot Apoorva Khare Bala Rajaratnam
+	The Weyl-Kac weight formula	2018	Gurbir Dhillon Apoorva Khare
+	The non-compact normed space of norms on a finite-dimensional Banach space	2018	Apoorva Khare
+	Generalized nil-Coxeter algebras	2018	Apoorva Khare
+	The Hoffmann–Jørgensen inequality in metric semigroups	2017	Apoorva Khare Bala Rajaratnam
+ PDF	Faces of highest weight modules and the universal Weyl polyhedron	2017	Gurbir Dhillon Apoorva Khare
+	Generalized nil-Coxeter algebras over discrete complex reflection groups	2017	Apoorva Khare
+ PDF	Generalized nil-Coxeter algebras, cocommutative algebras, and the PBW property	2017	Apoorva Khare
+	Total-positivity preservers	2017	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+ PDF	Erratum to “Standard parabolic subsets of highest weight modules”	2016	Apoorva Khare
+	Moment-sequence transforms	2016	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+	The Khinchin-Kahane inequality and Banach space embeddings for metric groups	2016	Apoorva Khare Bala Rajaratnam
+	Highest weight modules to first order	2016	Gurbir Dhillon Apoorva Khare
+	Characters of highest weight modules and integrability	2016	Gurbir Dhillon Apoorva Khare
+	Matrix positivity preservers in fixed dimension. I	2016	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+	Faces and maximizer subsets of highest weight modules	2016	Apoorva Khare
+	On the classification of finite-dimensional nil-Coxeter algebras over complex reflection groups	2016	Apoorva Khare
+	Model-free consistency of graph partitioning	2016	Peter Diao Dominique Guillot Apoorva Khare Bala Rajaratnam
+	The Khinchin-Kahane and Levy inequalities for abelian metric groups, and transfer from normed (abelian semi)groups to Banach spaces	2016	Apoorva Khare Bala Rajaratnam
+	On Category <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">O</mml:mi></mml:math> over triangular generalized Weyl algebras	2015	Apoorva Khare Akaki Tikaradze
+	Critical exponents of graphs	2015	Dominique Guillot Apoorva Khare Bala Rajaratnam
+	Preserving positivity for rank-constrained matrices	2015	Dominique Guillot Apoorva Khare Bala Rajaratnam
+	Schoenberg's positivity theorem in fixed dimension	2015	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar
+ PDF Chat	Standard parabolic subsets of highest weight modules	2015	Apoorva Khare
+	Differential calculus on graphon space	2015	Peter Diao Dominique Guillot Apoorva Khare Bala Rajaratnam
+	Preserving positivity for matrices with sparsity constraints	2015	Dominique Guillot Apoorva Khare Bala Rajaratnam
+	Integration and measures on the space of countable labelled graphs	2015	Apoorva Khare Bala Rajaratnam
+	Complete characterization of Hadamard powers preserving Loewner positivity, monotonicity, and convexity	2014	Dominique Guillot Apoorva Khare Bala Rajaratnam
+	ON FRACTIONAL HADAMARD POWERS OF POSITIVE BLOCK MATRICES	2014	Dominique Guillot Apoorva Khare Bala Rajaratnam
+	On fractional Hadamard powers of positive block matrices	2014	Dominique Guillot Apoorva Khare Bala Rajaratnam
+	Classification of measurable solutions of Cauchy's functional equations, and operators satisfying the Chain Rule	2013	Dominique Guillot Apoorva Khare Bala Rajaratnam
+	The critical exponent conjecture for powers of doubly nonnegative matrices	2013	Dominique Guillot Apoorva Khare Bala Rajaratnam
+	Loewner positive entrywise functions, and classification of measurable solutions of Cauchy's functional equations	2013	Dominique Guillot Apoorva Khare Bala Rajaratnam
+ PDF Chat	Representations of Complex Semi-simple Lie Groups and Lie Algebras	2013	Apoorva Khare
+	Weights of simple highest weight modules over a complex semisimple Lie algebra	2013	Apoorva Khare
+ PDF	The Sum of a Finite Group of Weights of a Hopf Algebra	2012	Apoorva Khare
+ PDF Chat	Solutions of several coupled discrete models in terms of Lamé polynomials of arbitrary order	2012	Avinash Khare Avadh Saxena Apoorva Khare
+	Representations of complex semi-simple Lie groups and Lie algebras	2012	Apoorva Khare
+	Faces of polytopes and Koszul algebras	2011	Vyjayanthi Chari Apoorva Khare Tim Ridenour
+ PDF Chat	Faces of Weight Polytopes and a Generalization of a Theorem of Vinberg	2010	Apoorva Khare Tim Ridenour
+ PDF Chat	Center and Representations of Infinitesimal Hecke Algebras of 𝔰𝔩<sub>2</sub>	2010	Akaki Tikaradze Apoorva Khare
+ PDF Chat	Functoriality of the BGG Category 𝒪††	2009	Apoorva Khare
+	Vector spaces as unions of proper subspaces	2009	Apoorva Khare
+	The covering problem for Chinese rings	2009	Apoorva Khare
+	Vector spaces, modules over Chinese rings, and monoids as unions of proper subobjects	2008	Apoorva Khare
+	DRINFELD-HECKE ALGEBRAS OVER COCOMMUTATIVE ALGEBRAS	2007	Apoorva Khare
+	Drinfeld-Hecke algebras over cocommutative algebras	2007	Apoorva Khare
+ PDF Chat	Quantized symplectic oscillator algebras of rank one	2006	Wee Liang Gan Apoorva Khare
+	Axiomatic framework for the BGG category $\mathcal{O}$	2005	Apoorva Khare
+	Category O over skew group rings	2005	Apoorva Khare
+	Axiomatic framework for the BGG category O	2005	Apoorva Khare
+	Erratum to “Category<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">O</mml:mi></mml:math>over a deformation of the symplectic oscillator algebra”	2004	Apoorva Khare
+	Category O over a deformation of the symplectic oscillator algebra	2004	Apoorva Khare
+	Divisibility tests and recurring decimals in Euclidean domains	2004	Apoorva Khare

Common Coauthors

Coauthor	Papers Together
Dominique Guillot	30
Bala Rajaratnam	19
Alexander C. R. Belton	18
Mihai Putinar	18
Projesh Nath Choudhury	9
Akaki Tikaradze	6
Gurbir Dhillon	5
Anna Lachowska	5
Sutanay Bhattacharya	3
Sujit Sakharam Damase	3
Tim Ridenour	2
Ludovick Bouthat	2
Peter Diao	2
Terence Tao	2
Frédéric Morneau-Guérin	2
Javad Mashreghi	2
Siddhartha Sahi	2
Alexander E. Hoffnung	1
G. Krishna Teja	1
Michiel Hazewinkel	1
Rafael González S. D'León	1
Alejandro H. Morales	1
Avadh Saxena	1
Tomasz Brzezi	1
Jacob Laan	1
Wee Liang Gan	1
Pintu Bhunia	1
Carolina Benedetti	1
Florin F. Nichita	1
M. Rajesh Kannan	1
Siddhartha Gadgil	1
Avinash Khare	1
T. A. Fritz	1
Martha Yip	1
Vamsi Pritham Pingali	1
Jon Links	1
Pace P. Nielsen	1
Simon A. Fairfax	1
Lior Silberman	1
Christopher R. H. Hanusa	1
Vyjayanthi Chari	1
K. Kanakoglou	1
Pamela E. Harris	1
Joel Lemay	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	On fractional Hadamard powers of positive definite matrices	1977	Carl H. Fitzgerald Roger A. Horn	18
+	Positive definite functions on spheres	1942	I. J. Schoenberg	17
+ PDF	The theory of infinitely divisible matrices and kernels	1969	Roger A. Horn	17
+	Bemerkungen zur Theorie der beschränkten Bilinearformen mit unendlich vielen Veränderlichen.	1911	Joan Brodsky Schur	15
+	Positive definite sequences and absolutely monotonic functions	1959	Walter Rudin	15
+	Complete characterization of Hadamard powers preserving Loewner positivity, monotonicity, and convexity	2014	Dominique Guillot Apoorva Khare Bala Rajaratnam	15
+	Matrix positivity preservers in fixed dimension. I	2016	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar	14
+ PDF Chat	On the sign patterns of entrywise positivity preservers in fixed dimension	2021	Apoorva Khare Terence Tao	13
+	Preserving positivity for rank-constrained matrices	2015	Dominique Guillot Apoorva Khare Bala Rajaratnam	13
+ PDF Chat	Monotonicity for entrywise functions of matrices	2009	Fumio Hiai	13
+	Introduction to Lie Algebras and Representation Theory	1972	James E. Humphreys	12
+	A reduction theorem for totally positive matrices	1952	Anne Whitney	10
+	Critical exponents of graphs	2015	Dominique Guillot Apoorva Khare Bala Rajaratnam	10
+ PDF Chat	KP solitons and total positivity for the Grassmannian	2014	Yuji Kodama Lauren Williams	10
+	Functions preserving positive definiteness for sparse matrices	2014	Dominique Guillot Bala Rajaratnam	10
+	Hadamard powers of some positive matrices	2016	Tanvi Jain	9
+	Positivity Preserving Hadamard Matrix Functions	2007	Rajendra Bhatia L. Elsner	9
+	Moment-sequence transforms	2016	Alexander C. R. Belton Dominique Guillot Apoorva Khare Mihai Putinar	9
+ PDF	The functions which operate on Fourier transforms	1959	Henry Helson Jean‐Pierre Kahane Yitzhak Katznelson Walter Rudin	9
+ PDF Chat	Retaining positive definiteness in thresholded matrices	2012	Dominique Guillot Bala Rajaratnam	8
+ PDF Chat	Continuous Hecke algebras	2005	Pavel Etingof Wee Liang Gan Victor Ginzburg	8
+	Generalized Thresholding of Large Covariance Matrices	2009	Adam Rothman Elizaveta Levina Ji Zhu	8
+ PDF Chat	Total Positivity: Tests and Parametrizations	2000	Sergey Fomin Andrei Zelevinsky	8
+	Hilbert Distances and Positive Definite Functions	1941	S. Bochner	8
+	Functions that preserve families of positive semidefinite matrices	1995	Carl H. Fitzgerald Charles A. Micchelli Allan Pinkus	8
+	Representations of Semisimple Lie Algebras in the BGG Category O	2008	James E. Humphreys	8
+	Category O over a deformation of the symplectic oscillator algebra	2004	Apoorva Khare	8
+ PDF	Critical exponents: old and new	2012	Charles R. Johnson Olivia Walch	8
+	Sur les fonctions absolument monotones	1929	Serge Bernstein	8
+	Über zwei Arten von Faktorenfolgen in der Theorie der algebraischen Gleichungen.	1914	J. Schur G. PɃlya	7
+	Preserving positivity for matrices with sparsity constraints	2015	Dominique Guillot Apoorva Khare Bala Rajaratnam	7
+ PDF	Large Networks and Graph Limits	2012	László Lovász	7
+	Covariance regularization by thresholding	2008	Peter J. Bickel Elizaveta Levina	7
+	Parametrizations of Canonical Bases and Totally Positive Matrices	1996	Arkady Berenstein Sergey Fomin Andrei Zelevinsky	7
+	Lectures on Quantum Groups	1995	Jens Carsten Jantzen	7
+	Total positivity of sums, Hadamard products and Hadamard powers: Results and counterexamples	2017	Shaun Fallat Charles R. Johnson Alan D. Sokal	7
+ PDF Chat	Large-Scale Correlation Screening	2011	Alfred O. Hero Bala Rajaratnam	7
+	Combinatorics and total positivity	1995	Francesco Brenti	7
+	Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems	2002	Felix R. Gantmacher M. Г. Крейн	7
+	Faces and maximizer subsets of highest weight modules	2016	Apoorva Khare	7
+ PDF	Functions operating on positive definite matrices and a theorem of Schoenberg	1978	Jens Peter Christensen Paul Ressel	7
+	Totally positive matrices	1987	T. Andô	7
+	Finite dimensional algebras and highest weight categories.	1988	Edward Cline Brian Parshall Leonard Scott	6
+	Total positivity, Grassmannians, and networks	2006	Alexander Postnikov	6
+ PDF	The inversion of a general class of convolution transforms	1949	I. I. Hirschman D. V. Widder	6
+ PDF	Double Bruhat cells and total positivity	1999	Sergey Fomin Andrei Zelevinsky	6
+ PDF	Sampling theorems for shift-invariant spaces, Gabor frames, and totally positive functions	2017	Karlheinz Gröchenig José Luis Romero Joachim Stöckler	6
+	Sur les matrices complètement non négatives et oscillatoires	1937	F.R. GANTMAKHER M. Г. Крейн	6
+	Total Positivity and Its Applications	1996	M. Gasca Charles A. Micchelli	6
+ PDF	KP solitons, total positivity, and cluster algebras	2011	Yuji Kodama Lauren Williams	6