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We study the class of Lorentzian polynomials.
1906
Earlier work this paper cites.
Rudolf Heine, Der Wertvorrat der gemischten Inhalte von zwei, drei und vier ebenen Eibereichen . Math. Ann. 115
1938
Earlier work this paper cites.
Isaac Jacob Schoenberg, Metric spaces and positive definite functions . Trans. Amer. Math. Soc. 44
1938
Earlier work this paper cites.
Geoffrey Shephard, Inequalities between mixed volumes of convex sets . Mathematika 7
1960
Earlier work this paper cites.
Samuel Karlin, Total positivity. Vol. I. Stanford University Press, Stanford, 1968
1968
Earlier work this paper cites.
Wim Nuij, A note on hyperbolic polynomials . Math. Scand. 23
1968
Earlier work this paper cites.
Korandattil Venugopalan Menon, On the convolution of logarithmically concave sequences . Proc. Amer. Math. Soc. 23
1969
Earlier work this paper cites.
Cornelius Fortuin and Pieter Kasteleyn, On the random-cluster model. I. Introduction and relation to other models. Physica 57
1972
Earlier work this paper cites.
Thomas Markham, Nonnegative matrices whose inverses are M M -matrices . Proc. Amer. Math. Soc. 36
1972
Earlier work this paper cites.
John Mason, Matroids: unimodal conjectures and Motzkin’s theorem . Combinatorics (Proc. Conf. Combinatorial Math., Math. Inst., Oxford, 1972), 207–220, Inst. Math. Appl., Southend-on-Sea, 1972
1972
Earlier work this paper cites.
Paul Seymour, Matroids, hypergraphs, and the max-flow min-cut theorem . Thesis, University of Oxford, 1975
1975
Earlier work this paper cites.
Paul Seymour and Dominic Welsh, Combinatorial applications of an inequality from statistical mechanics . Math. Proc. Cambridge Philos. Soc. 77
1975
Earlier work this paper cites.
Dominic Welsh, Matroid theory . London Mathematical Society Monographs 8
1976
Earlier work this paper cites.
Robin Hartshorne, Algebraic geometry . Graduate Texts in Mathematics 52
1977
Earlier work this paper cites.
Shing Tung Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge–Ampère equation. I. Comm. Pure Appl. Math. 31
1978
Earlier work this paper cites.
Thomas Dowling, On the independent set numbers of a finite matroid . Combinatorics 79 (Proc. Colloq., Univ. Montrál, Montreal, Que., 1979), Part I. Ann. Discrete Math. 8
1980
Earlier work this paper cites.
Jiří Gregor, On quadratic Hurwitz forms. I . Apl. Mat. 26
1981
Earlier work this paper cites.
Elliott Lieb and Alan Sokal, A general Lee–Yang theorem for one-component and multicomponent ferromagnets . Comm. Math. Phys. 80
1981
Earlier work this paper cites.
Aleksandr Timan and Igor Vestfrid, Any separable ultrametric space is isometrically embeddable in ℓ 2 \ell_{2} . Funktsional. Anal. i Prilozhen. 17
1983
Earlier work this paper cites.
Christian Berg, Jens Christensen, and Paul Ressel, Harmonic analysis on semigroups. Theory of positive definite and related functions . Graduate Texts in Mathematics 100
1984
Earlier work this paper cites.
Carolyn Mahoney, On the unimodality of the independent set numbers of a class of matroids . J. Combin. Theory Ser. B 39
1985
Earlier work this paper cites.
Cui Kui Zhao, A conjecture on matroids . Neimenggu Daxue Xuebao 16
1985
Earlier work this paper cites.
Yahya Ould Hamidoune and Isabelle Salaün, On the independence numbers of a matroid . J. Combin. Theory Ser. B 47
1989
Earlier work this paper cites.
Tomás Feder and Milena Mihail, Balanced matroids , Proceedings of the 24th Annual ACM Symposium on Theory of Computing, 26–38, ACM Press, 1992
1992
Earlier work this paper cites.
William Fulton, Introduction to toric varieties . Annals of Mathematics Studies 131
1993
Earlier work this paper cites.
Abraham Berman, and Robert Plemmons, Nonnegative matrices in the mathematical sciences . Revised reprint of the 1979 original. Classics in Applied Mathematics 9
1994
Cited alongside, same era.
Roger Horn and Charles Johnson, Topics in matrix analysis . Cambridge University Press, Cambridge, 1994
1994
Cited alongside, same era.
Ravindra Bapat and Tirukkannamangai Raghavan, Nonnegative matrices and applications . Encyclopedia of Mathematics and its Applications 64
1997
Cited alongside, same era.
Thomas Liggett, Ultra log-concave sequences and negative dependence . J. Comb. Th. A 79
1997
Cited alongside, same era.
William Fulton, Intersection theory . Second edition. Ergebnisse der Mathematik und ihrer Grenzgebiete 3
1998
Cited alongside, same era.
Julius Borcea and Petter Brändén, The Lee–Yang and Pólya–Schur programs. I. Linear operators preserving stability . Invent. Math. 177
2009
Later among the works it cites.
Julius Borcea, Petter Brändén, and Thomas Liggett, Negative dependence and the geometry of polynomials . J. Amer. Math. Soc. 22
2009
Later among the works it cites.
Leonid Gurvits, On multivariate Newton-like inequalities . Advances in combinatorial mathematics, 61–78, Springer, Berlin, 2009
2009
Later among the works it cites.
Alexander Postnikov, Permutohedra, associahedra, and beyond . Int. Math. Res. Not. IMRN 2009, no. 6, 1026–1106
2009
Later among the works it cites.
Julius Borcea and Petter Brändén, Multivariate Pólya–Schur classification problems in the Weyl algebra . Proc. Lond. Math. Soc. 101
2010
Later among the works it cites.
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Jeff Kahn, A normal law for matchings. Combinatorica 20
2000
Cited alongside, same era.
Robin Pemantle, Towards a theory of negative dependence . J. Math. Phys., 41
2000
Cited alongside, same era.
Jürgen Herzog and Takayuki Hibi, Discrete polymatroids . J. Algebraic Combin. 16
2002
Cited alongside, same era.
David Marker, Model theory: An introduction . Graduate Texts in Mathematics 217
2002
Cited alongside, same era.
Kazuo Murota, Discrete convex analysis . SIAM Monographs on Discrete Mathematics and Applications. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2003
2003
Cited alongside, same era.
Youngbin Choe, James Oxley, Alan Sokal, and David Wagner, Homogeneous multivariate polynomials with the half-plane property . Adv. in Appl. Math. 32
2004
Cited alongside, same era.
Geoffrey Grimmett and Stephan Winkler, Negative association in uniform forests and connected graphs. Random Structures Algorithms 24
2004
Cited alongside, same era.
Petter Brändén, Discrete concavity and the half-plane property , Siam J. Discrete Math. 24
2010
Later among the works it cites.
Jeff Kahn and Michael Neiman, Negative correlation and log-concavity . Random Structures Algorithms 37
2010
Later among the works it cites.
Thomas Liggett, Continuous time Markov processes. An introduction . Graduate Studies in Mathematics 113
2010
Later among the works it cites.
Denis Serre, Matrices. Theory and applications . Graduate Texts in Mathematics 216
2010
Later among the works it cites.
Jeff Kahn and Michael Neiman, A strong log-concavity property for measures on Boolean algebras . J. Combin. Theory Ser. A 118
2011
Later among the works it cites.
James Oxley, Matroid theory . Second edition. Oxford Graduate Texts in Mathematics 21
2011
Later among the works it cites.
David Wagner, Multivariate stable polynomials: theory and applications . Bull. Amer. Math. Soc. (N.S.) 48
2011
Later among the works it cites.
June Huh and Eric Katz, Log-concavity of characteristic polynomials and the Bergman fan of matroids . Math. Ann. 354
2012
Later among the works it cites.
Robin Pemantle, Hyperbolicity and stable polynomials in combinatorics and probability . Current developments in mathematics, 2011, 57–123, Int. Press, Somerville, MA, 2012
2012
Later among the works it cites.
Akiyoshi Shioura, Matroid rank functions and discrete concavity . Jpn. J. Ind. Appl. Math. 29
2012
Later among the works it cites.
Matthias Lenz, The f-vector of a representable-matroid complex is log-concave . Adv. in Appl. Math. 51
2013
Later among the works it cites.
Claude Dellacherie, Servet Martinez, and Jaime San Martin, Inverse M-matrices and ultrametric matrices . Lecture Notes in Mathematics 2118
2014
Later among the works it cites.
Rolf Schneider, Convex bodies: the Brunn–Minkowski theory . Second expanded edition. Encyclopedia of Mathematics and its Applications 151
2014
Later among the works it cites.
Diane Maclagan and Bernd Sturmfels, Introduction to tropical geometry . Graduate Studies in Mathematics 161
2015
Later among the works it cites.
June Huh and Botong Wang, Enumeration of points, lines, planes, etc. Acta Math. 218
2017
Later among the works it cites.
Brian Lehmann and Jian Xiao, Correspondences between convex geometry and complex geometry . Épijournal de Géométrie Algébrique 1
2017
Later among the works it cites.
Karim Adiprasito, June Huh, and Eric Katz, Hodge theory for combinatorial geometries . Ann. of Math. (2) 188
2018
Later among the works it cites.
June Huh, Combinatorial applications of the Hodge–Riemann relations . Proceedings of the International Congress of Mathematicians 3
2018
Later among the works it cites.
Pavel Galashin, Steven N. Karp, and Thomas Lam, The totally nonnegative part of G / P G/P is a ball . Adv. in Math. 351
2019
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2020
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