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Mathematics Magazine Volume 82, 2009 - Issue 3
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Original Articles

Tropical Mathematics

David SpeyerMassachusetts Institute of TechnologyCambridge, [email protected]
&
Bernd SturmfelsUniversity of California at BerkeleyBerkeley, [email protected]
Pages 163-173 | Published online: 16 Apr 2018

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B. Sury. (2023) A Tropical Power Sum. Mathematics Magazine 96:2, pages 153-156.
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K. Ahmed, S. Pal & R. Mohan. (2023) A review of the tropical approach in cryptography. Cryptologia 47:1, pages 63-87.
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K. Ahmed, S. Pal & R. Mohan. (2023) Key exchange protocol based upon a modified tropical structure. Communications in Algebra 51:1, pages 214-223.
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Ludwig Baringhaus & Rudolf Grübel. (2021) Mixture representations of noncentral distributions. Communications in Statistics - Theory and Methods 50:24, pages 5997-6013.
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M. J. de la Puente. (2020) Quasi-Euclidean classification of alcoved convex polyhedra. Linear and Multilinear Algebra 68:10, pages 2110-2142.
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N. Krivulin. (2017) Tropical optimization problems in time-constrained project scheduling. Optimization 66:2, pages 205-224.
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AndreasW. M. Dress & Walter Wenzel. (2015) Arithmetic and Polynomials over Fuzzy Rings. Communications in Algebra 43:3, pages 1207-1231.
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Erwan Brugallé & Kristin Shaw. (2014) A Bit of Tropical Geometry. The American Mathematical Monthly 121:7, pages 563-589.
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Huawei Huang, Weisha Kong & Ting Xu. (2024) Asymmetric Cryptography Based on the Tropical Jones Matrix. Symmetry 16:4, pages 456.
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Iryna Chernega, Mariia Martsinkiv, Taras Vasylyshyn & Andriy Zagorodnyuk. (2023) Applications of Supersymmetric Polynomials in Statistical Quantum Physics. Quantum Reports 5:4, pages 683-697.
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David Barnhill & Ruriko Yoshida. (2023) Clustering Methods over the Tropical Projective Torus. Mathematics 11:15, pages 3433.
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Ruriko Yoshida. (2023) Imputing Phylogenetic Trees Using Tropical Polytopes over the Space of Phylogenetic Trees. Mathematics 11:15, pages 3419.
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Keiji Miura & Ruriko Yoshida. (2023) Plücker coordinates of the best-fit Stiefel tropical linear space to a mixture of Gaussian distributions. Information Geometry 6:1, pages 171-201.
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José Antonio Martínez, Ana Belén Castaño-Fernández & María Luz Puertas. (2022) The 2-domination number of cylindrical graphs. Computational and Applied Mathematics 41:8.
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Soichiro Fujii, Yuni Iwamasa & Kei Kimura. (2022) Quantaloidal Approach to Constraint Satisfaction. Electronic Proceedings in Theoretical Computer Science 372, pages 289-305.
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Ester M. Garzón, José Antonio Martínez, Juan José Moreno & María Luz Puertas. (2022) HPC acceleration of large (min, +) matrix products to compute domination-type parameters in graphs. The Journal of Supercomputing 78:16, pages 17826-17843.
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Bo Lin, Anthea Monod & Ruriko Yoshida. (2022) Tropical Geometric Variation of Tree Shapes. Discrete & Computational Geometry 68:3, pages 817-849.
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Kashif Ahmed, Saibal Pal & Radha Mohan. (2021) Some new semiring structures. Asian-European Journal of Mathematics 15:09.
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Huawei Huang, Chunhua Li & Lunzhi Deng. (2022) Public-Key Cryptography Based on Tropical Circular Matrices. Applied Sciences 12:15, pages 7401.
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Tai-Danae Bradley, John Terilla & Yiannis Vlassopoulos. (2022) An Enriched Category Theory of Language: From Syntax to Semantics. La Matematica 1:2, pages 551-580.
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Ruriko Yoshida & Shelby Cox. (2022) Tree Topologies along a Tropical Line Segment. Vietnam Journal of Mathematics 50:2, pages 395-419.
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Ruriko Yoshida. 2022. Intelligent Systems and Applications. Intelligent Systems and Applications 340 361 .
Ruriko Yoshida. (2021) Tropical Balls and Its Applications to K Nearest Neighbor over the Space of Phylogenetic Trees. Mathematics 9:7, pages 779.
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Sara Kališnik & Davorin Lešnik. (2021) Symmetric polynomials in upper-bound semirings. Journal of Symbolic Computation 103, pages 280-299.
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C. J. Chapman & H. P. Wynn. (2021) Fractional power series and the method of dominant balances. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477:2246, pages 20200646.
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Victor Alexeevich Bykovskii & M A Romanov. (2021) Полиномиальные последовательности СомосаPolynomial Somos Sequences. Функциональный анализ и его приложения Funktsional'nyi Analiz i ego Prilozheniya 55:1, pages 20-32.
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V. A. Bykovskii & M. A. Romanov. (2021) Polynomial Somos Sequences. Functional Analysis and Its Applications 55:1, pages 15-25.
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S. Northshield. (2020) Tropical cycles. The Mathematical Gazette 104:560, pages 225-234.
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Haipeng Peng, Mengwei He, Lixiang Li & Yixian Yang. (2020) A New Lightweight Key Exchange Protocol Based on T—tensor Product. A New Lightweight Key Exchange Protocol Based on T—tensor Product.
Luyan Yu. (2020) Extreme rays of the ℓ∞-nearest ultrametric tropical polytope. Linear Algebra and its Applications 587, pages 23-44.
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Sara Kališnik & Davorin Lešnik. (2019) Symmetric polynomials in tropical algebra semirings. Journal of Symbolic Computation 93, pages 100-119.
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Peter Butkovič. (2018) A Note on Tropical Linear and Integer Programs. Journal of Optimization Theory and Applications 180:3, pages 1011-1026.
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Atsuo Kuniba & Masato Okado. (2019) Set-theoretical solutions to the reflection equation associated to the quantum affine algebra of type $\boldsymbol{A^{(1)}_{n-1}}$. Journal of Integrable Systems 4:1.
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Giovanni Albini & Marco Paolo Bernardi. 2019. Mathematics and Computation in Music. Mathematics and Computation in Music 73 83 .
Hoon Hong & J. Rafael Sendra. (2018) Number of common roots and resultant of two tropical univariate polynomials. Journal of Algebra 511, pages 420-439.
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Jaiung Jun. (2018) Valuations of semirings. Journal of Pure and Applied Algebra 222:8, pages 2063-2088.
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Andrew Gitlin. (2018) New examples of dimension zero categories. Journal of Algebra 505, pages 271-278.
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Peter Butkovič. (2018) On integer images of max-plus linear mappings. Discrete Applied Mathematics 239, pages 62-74.
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Qiwen Kang & Ruriko Yoshida. 2018. Mathematical Software – ICMS 2018. Mathematical Software – ICMS 2018 272 279 .
Yaroslav Shitov. (2017) Which semifields are exact?. Journal of Algebra 492, pages 393-401.
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Hoon Hong, Yonggu Kim, Georgy Scholten & J. Rafael Sendra. (2017) Resultants over commutative idempotent semirings I: Algebraic aspect. Journal of Symbolic Computation 79, pages 285-308.
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Agnese Baldisserri & Elena Rubei. (2017) A characterization of dissimilarity families of trees. Discrete Applied Mathematics 220, pages 35-45.
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Aaron Bertram & Robert Easton. (2017) The tropical Nullstellensatz for congruences. Advances in Mathematics 308, pages 36-82.
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Gunnar Carlsson & Sara Kališnik Verovšek. (2016) Symmetric and r-symmetric tropical polynomials and rational functions. Journal of Pure and Applied Algebra 220:11, pages 3610-3627.
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Risto Korhonen & Kazuya Tohge. (2016) Second main theorem in the tropical projective space. Advances in Mathematics 298, pages 693-725.
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Peter Butkovič. (2016) On tropical supereigenvectors. Linear Algebra and its Applications 498, pages 574-591.
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J. Linde & M.J. de la Puente. (2015) Matrices commuting with a given normal tropical matrix. Linear Algebra and its Applications 482, pages 101-121.
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Zur Izhakian, Manfred Knebusch & Louis Rowen. (2014) Layered tropical mathematics. Journal of Algebra 416, pages 200-273.
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