Ardila-Mantilla, Federico; Cordero Aguilar, Mont The degree of a tropical root surface of type A. (English) Zbl 07948614 Orbita Math. 2, No. 1, 33-42 (2025). MSC: 14T05 05E14 14T15 17B22 52B05 52B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Soprunov, Ivan; Soprunova, Jenya The volume polynomial of lattice polygons. (English) Zbl 07962905 Proc. Am. Math. Soc. 152, No. 12, 5313-5325 (2024). MSC: 52B20 52A39 11H55 14T10 14M25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Brandenburg, Marie-Charlotte; Loho, Georg; Sinn, Rainer Corrigendum to: “Tropical positivity and determinantal varieties”. (English) Zbl 1541.14087 Algebr. Comb. 7, No. 3, 749-751 (2024). MSC: 14T15 14P05 14M12 05E14 52B40 × Cite Format Result Cite Review PDF Full Text: DOI
Boretsky, Jonathan; Eur, Christopher; Williams, Lauren Polyhedral and tropical geometry of flag positroids. (English) Zbl 07865172 Algebra Number Theory 18, No. 7, 1333-1374 (2024). MSC: 14T15 05Exx × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Brandenburg, Marie-Charlotte; Loho, Georg; Sinn, Rainer Tropical positivity and determinantal varieties. (English) Zbl 1537.14087 Algebr. Comb. 6, No. 4, 999-1040 (2023); corrigendum ibid. 7, No. 3, 749-751 (2024). Reviewer: Keyvan Yaghmayi (Salt Lake City) MSC: 14T15 14P05 14M12 05E14 52B40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Krasikov, Vitaly A. A survey on computational aspects of polynomial amoebas. (English) Zbl 07734146 Math. Comput. Sci. 17, No. 3-4, Paper No. 16, 19 p. (2023). Reviewer: Mikhail Shkolnikov (Sofia) MSC: 14J81 14P25 14Q15 14T90 32A08 68W40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
de Jong, Robin; Shokrieh, Farbod Tropical moments of tropical Jacobians. (English) Zbl 1520.14114 Can. J. Math. 75, No. 4, 1045-1075 (2023). Reviewer: Guoquan Gao (Beijing) MSC: 14T15 14G40 11G50 94C05 52C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Brandenburg, Marie-Charlotte; Haase, Christian; Tran, Ngoc Mai Competitive equilibrium always exists for combinatorial auctions with graphical pricing schemes. (English) Zbl 1509.91025 Matematica 2, No. 1, 1-30 (2023). MSC: 91B26 52B20 14T90 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Panzer, Erik Hepp’s bound for Feynman graphs and matroids. (English) Zbl 1520.81076 Ann. Inst. Henri Poincaré D, Comb. Phys. Interact. 10, No. 1, 31-119 (2023). Reviewer: Michael Borinsky (Zürich) MSC: 81Q30 81T18 81T15 14T90 05B35 52B40 51M20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Agostini, Daniele; Fevola, Claudia; Mandelshtam, Yelena; Sturmfels, Bernd KP solitons from tropical limits. (English) Zbl 1495.14046 J. Symb. Comput. 114, 282-301 (2023). Reviewer: Ahmed Lesfari (El Jadida) MSC: 14H42 14T90 37K10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Montúfar, Guido; Ren, Yue; Zhang, Leon Sharp bounds for the number of regions of maxout networks and vertices of Minkowski sums. (English) Zbl 1538.68010 SIAM J. Appl. Algebra Geom. 6, No. 4, 618-649 (2022). MSC: 68Q06 06A07 14T15 52B05 52C35 68Q07 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dickenstein, Alicia; Herrero, María Isabel; Mourrain, Bernard Curve valuations and mixed volumes in the implicitization of rational varieties. (English) Zbl 1502.14124 J. Algebra 612, 691-721 (2022). Reviewer: Rick Rischter (Itajubá) MSC: 14M25 14T15 68W30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Casals, Roger; Vianna, Renato Full ellipsoid embeddings and toric mutations. (English) Zbl 1534.53074 Sel. Math., New Ser. 28, No. 3, Paper No. 61, 62 p. (2022). Reviewer: Sergiy Koshkin (Houston) MSC: 53D35 53D05 14M25 14T20 13F60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Clarke, Oliver; Higashitani, Akihiro; Mohammadi, Fatemeh Combinatorial mutations and block diagonal polytopes. (English) Zbl 1493.14071 Collect. Math. 73, No. 2, 305-335 (2022). Reviewer: Keyvan Yaghmayi (Salt Lake City) MSC: 14M15 13P10 14M25 14T99 52B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kazarnovskii, Boris Ya. The quasi-algebraic ring of conditions of \(\mathbb{C}^n\). (English. Russian original) Zbl 1490.14100 Izv. Math. 86, No. 1, 169-202 (2022); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 86, No. 1, 180-218 (2022). MSC: 14T15 14C17 52A30 14M25 × Cite Format Result Cite Review PDF Full Text: DOI
Antipova, Irina Avgustovna; Kleshkova, Ekaterina Andreevna On facets of the Newton polytope for the discriminant of the polynomial system. (English) Zbl 1475.14094 Sib. Èlektron. Mat. Izv. 18, No. 2, 1180-1188 (2021). MSC: 14M25 14T15 32S25 13P15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mészáros, Karola; Setiabrata, Linus Lorentzian polynomials from polytope projections. (English) Zbl 1473.52021 Algebr. Comb. 4, No. 4, 723-739 (2021). MSC: 52B40 05A20 14T15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kazarnovskii, Boris Ya; Khovanskii, Askold G.; Esterov, Alexander I. Newton polytopes and tropical geometry. (English. Russian original) Zbl 1476.14087 Russ. Math. Surv. 76, No. 1, 91-175 (2021); translation from Usp. Mat. Nauk 76, No. 1, 95-190 (2021). Reviewer: Felix Röhrle (Frankfurt am Main) MSC: 14M25 14T15 14C17 × Cite Format Result Cite Review PDF Full Text: DOI
Obatake, Nida; Shiu, Anne; Sofia, Dilruba Mixed volume of small reaction networks. (English) Zbl 1470.92410 Involve 13, No. 5, 845-860 (2020). Reviewer: Dieter Erle (Dortmund) MSC: 92E20 65H14 14Q30 14T90 14M25 52B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Falkensteiner, Sebastian; Garay-López, Cristhian; Haiech, Mercedes; Noordman, Marc Paul; Toghani, Zeinab; Boulier, François The fundamental theorem of tropical partial differential algebraic geometry. (English) Zbl 1477.14096 Mantzaflaris, Angelos (ed.), Proceedings of the 45th international symposium on symbolic and algebraic computation, ISSAC ’20, Kalamata, Greece, July 20–23, 2020. New York, NY: Association for Computing Machinery (ACM). 178-185 (2020). MSC: 14T10 14T90 68W30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
de la Puente, María Jesús; Clavería, Pedro Luis Isocanted alcoved polytopes. (English) Zbl 1549.52013 Appl. Math., Praha 65, No. 6, 703-726 (2020). MSC: 52B12 15A80 52B05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Brysiewicz, Taylor Numerical software to compute Newton polytopes and tropical membership. (English) Zbl 1474.14002 Math. Comput. Sci. 14, No. 3, 577-589 (2020). MSC: 14-04 14M25 65H20 14T15 14Q99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhou, Peng Lagrangian skeleta of hypersurfaces in \((\mathbb{C}^*)^n\). (English) Zbl 1439.53077 Sel. Math., New Ser. 26, No. 2, Paper No. 26, 33 p. (2020). MSC: 53D37 14T99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fang, Xin; Fourier, Ghislain; Litza, Jan-Philipp; Pegel, Christoph A continuous family of marked poset polytopes. (English) Zbl 1445.52009 SIAM J. Discrete Math. 34, No. 1, 611-639 (2020). Reviewer: Matthias Beck (San Francisco) MSC: 52B20 06A07 52B05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tran, Ngoc Mai; Yu, Josephine Product-mix auctions and tropical geometry. (English) Zbl 1434.91033 Math. Oper. Res. 44, No. 4, 1396-1411 (2019). MSC: 91B26 90C24 14T90 90C10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nisse, Mounir; Sadykov, Timur Amoeba-shaped polyhedral complex of an algebraic hypersurface. (English) Zbl 1423.32010 J. Geom. Anal. 29, No. 2, 1356-1368 (2019). Reviewer: Piotr Pokora (Kraków) MSC: 32A60 32B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Schröter, Benjamin Multi-splits and tropical linear spaces from nested matroids. (English) Zbl 1472.52019 Discrete Comput. Geom. 61, No. 3, 661-685 (2019). MSC: 52B40 05A18 14T15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Shitov, Ya. N. Tropical lower bound for extended formulations. II: Deficiency graphs of matrices. (English. Russian original) Zbl 1409.15014 Izv. Math. 83, No. 1, 184-195 (2019); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 83, No. 1, 203-216 (2019). MSC: 15A80 14T05 05C50 15A23 15B48 52B05 × Cite Format Result Cite Review PDF Full Text: DOI
Fink, Alex; Moci, Luca Polyhedra and parameter spaces for matroids over valuation rings. (English) Zbl 1439.52014 Adv. Math. 343, 448-494 (2019). MSC: 52B40 05B35 14T10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Esterov, Alexander Characteristic classes of affine varieties and Plücker formulas for affine morphisms. (English) Zbl 1472.14006 J. Eur. Math. Soc. (JEMS) 20, No. 1, 15-59 (2018). MSC: 14C17 32M10 14T15 14M25 14M10 14N15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Manjunath, Madhusudan Syzygies over the polytope semiring. (English) Zbl 1393.13030 J. Lond. Math. Soc., II. Ser. 96, No. 2, 482-500 (2017). Reviewer: Georg Loho (Berlin) MSC: 13D02 14T05 16E05 16Y60 52B20 52B11 15A80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Lin, Bo; Sturmfels, Bernd; Tang, Xiaoxian; Yoshida, Ruriko Convexity in tree spaces. (English) Zbl 1370.05040 SIAM J. Discrete Math. 31, No. 3, 2015-2038 (2017). MSC: 05C05 30F45 52B40 68U05 92D15 52A99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Alekseev, Anton; Podkopaeva, Masha; Szenes, Andras A symplectic proof of the Horn inequalities. (English) Zbl 1372.15011 Adv. Math. 318, 711-736 (2017). MSC: 15A42 15B57 15A80 14T05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Joswig, Michael; Schröter, Benjamin Matroids from hypersimplex splits. (English) Zbl 1366.05024 J. Comb. Theory, Ser. A 151, 254-284 (2017). MSC: 05B35 52B40 14T99 14M15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bliss, Nathan; Verschelde, Jan Computing all space curve solutions of polynomial systems by polyhedral methods. (English) Zbl 1453.13084 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 18th international workshop, CASC 2016, Bucharest, Romania, September 19–23, 2016. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9890, 73-86 (2016). MSC: 13P15 14M25 14T15 65H10 65H20 68W30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Jensen, Anders; Yu, Josephine Stable intersections of tropical varieties. (English) Zbl 1406.14045 J. Algebr. Comb. 43, No. 1, 101-128 (2016). MSC: 14T05 14C17 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Shitov, Yaroslav Tropical lower bounds for extended formulations. (English) Zbl 1331.15021 Math. Program. 153, No. 1 (B), 67-74 (2015). Reviewer: John D. Dixon (Ottawa) MSC: 15A80 52B55 15A23 15B48 × Cite Format Result Cite Review PDF Full Text: DOI
Linde, J.; de la Puente, M. J. Matrices commuting with a given normal tropical matrix. (English) Zbl 1321.15046 Linear Algebra Appl. 482, 101-121 (2015). MSC: 15A80 14T05 15B57 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fink, Alex; Rincón, Felipe Stiefel tropical linear spaces. (English) Zbl 1321.15044 J. Comb. Theory, Ser. A 135, 291-331 (2015). MSC: 15A80 14T05 52B40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gajula, Sailaja; Soprunov, Ivan; Soprunova, Jenya Tropical determinant on transportation polytopes. (English) Zbl 1312.90040 Linear Algebra Appl. 475, 28-44 (2015). MSC: 90C10 52B12 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kazarnovskii, B. Ya. On the action of the complex Monge-Ampère operator on piecewise linear functions. (English. Russian original) Zbl 1304.32028 Funct. Anal. Appl. 48, No. 1, 15-23 (2014); translation from Funkts. Anal. Prilozh. 48, No. 1, 19-29 (2014). MSC: 32W20 × Cite Format Result Cite Review PDF Full Text: DOI
Kambites, Mark; Johnson, Marianne Idempotent tropical matrices and finite metric spaces. (English) Zbl 1310.14050 Adv. Geom. 14, No. 2, 253-276 (2014). MSC: 14T05 16Y60 20H99 20M10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Adrovic, Danko; Verschelde, Jan Polyhedral methods for space curves exploiting symmetry applied to the cyclic \(n\)-roots problem. (English) Zbl 1412.13030 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 15th international workshop, CASC 2013, Berlin, Germany, September 9–13, 2013. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 8136, 10-29 (2013). MSC: 13P15 68W30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Jensen, Anders; Yu, Josephine Computing tropical resultants. (English) Zbl 1316.14117 J. Algebra 387, 287-319 (2013). Reviewer: Thanh Vu (Lincoln) MSC: 14T05 14M25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cattani, Eduardo; Cueto, María Angélica; Dickenstein, Alicia; Di Rocco, Sandra; Sturmfels, Bernd Mixed discriminants. (English) Zbl 1273.13051 Math. Z. 274, No. 3-4, 761-778 (2013). Reviewer: Marcel Morales (Saint-Martin-d’Hères) MSC: 13P15 14M25 14T05 52B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cueto, María Angélica; Lin, Shaowei Tropical secant graphs of monomial curves. (English) Zbl 1284.14083 Beitr. Algebra Geom. 54, No. 1, 383-418 (2013). Reviewer: Ivan Bazhov (Carouge) MSC: 14Q05 14T05 14M25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Fink, Alex Tropical cycles and Chow polytopes. (English) Zbl 1282.14106 Beitr. Algebra Geom. 54, No. 1, 13-40 (2013). Reviewer: Ivan Bazhov (Carouge) MSC: 14T05 52B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rincón, Felipe Computing tropical linear spaces. (English) Zbl 1319.14060 J. Symb. Comput. 51, 86-98 (2013). MSC: 14T05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Adrovic, Danko; Verschelde, Jan Computing Puiseux series for algebraic surfaces. (English) Zbl 1323.68578 van der Hoeven, Joris (ed.) et al., Proceedings of the 37th international symposium on symbolic and algebraic computation, ISSAC 2012, Grenoble, France, July 22–25, 2012. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-1269-1). 20-27 (2012). MSC: 68W30 13P15 14Q10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dinitz, Thomas; Hartman, Matthew; Soprunova, Jenya Tropical determinant of integer doubly-stochastic matrices. (English) Zbl 1242.15032 Linear Algebra Appl. 436, No. 5, 1212-1227 (2012). Reviewer: Huang Wenxue (Scarborough) MSC: 15B51 52B12 90C10 15A15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Markwig, Hannah; Markwig, Thomas; Shustin, Eugenii Tropical curves with a singularity in a fixed point. (English) Zbl 1254.14070 Manuscr. Math. 137, No. 3-4, 383-418 (2012). Reviewer: Alexander Esterov (Moscow) MSC: 14T05 51M20 05B35 14H20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rincón, Felipe Isotropical linear spaces and valuated Delta-matroids. (English) Zbl 1232.05040 J. Comb. Theory, Ser. A 119, No. 1, 14-32 (2012). MSC: 05B20 52B40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Iriarte Giraldo, Benjamin Dissimilarity vectors of trees and their tropical linear spaces (extended abstract). (English. French summary) Zbl 1355.14038 Proceedings of the 23rd international conference on formal power series and algebraic combinatorics, FPSAC 2011, Reykjavik, Iceland, June 13–17, 2011. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Mathematics and Theoretical Computer Science. Proceedings, 375-386 (2011). MSC: 14T05 × Cite Format Result Cite Review PDF Full Text: Link
Nisse, Mounir Complex tropical localization, and coamoebas of complex algebraic hypersurfaces. (English) Zbl 1235.14058 Gurvits, Leonid (ed.) et al., Randomization, relaxation, and complexity in polynomial equation solving. Banff International Research Station workshop on randomization, relaxation, and complexity, Banff, Ontario, Canada, February 28–March 5, 2010. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-5228-6/pbk). Contemporary Mathematics 556, 127-144 (2011). Reviewer: Eugenii I. Shustin (Tel Aviv) MSC: 14T05 32A60 × Cite Format Result Cite Review PDF Full Text: arXiv
Herrmann, Sven On the facets of the secondary polytope. (English) Zbl 1228.52008 J. Comb. Theory, Ser. A 118, No. 2, 425-447 (2011). Reviewer: Anna Romanowska (Warsaw) MSC: 52B40 05B35 52B05 14T05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Allamigeon, Xavier; Gaubert, Stéphane; Katz, Ricardo D. The number of extreme points of tropical polyhedra. (English) Zbl 1246.14078 J. Comb. Theory, Ser. A 118, No. 1, 162-189 (2011). Reviewer: Serge Lawrencenko (Moskva) MSC: 14T05 52A01 52B05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cueto, María Angélica; Lin, Shaowei Tropical secant graphs of monomial curves. (English. French summary) Zbl 1373.05213 Proceedings of the 22nd annual international conference on formal power series and algebraic combinatorics, FPSAC 2010, San Francisco, USA, August 2–6, 2010. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Mathematics and Theoretical Computer Science. Proceedings, 669-680 (2010). MSC: 05E15 14T99 × Cite Format Result Cite Review PDF Full Text: Link
Cueto, María Angélica; Tobis, Enrique A.; Yu, Josephine An implicitization challenge for binary factor analysis. (English) Zbl 1203.14057 J. Symb. Comput. 45, No. 12, 1296-1315 (2010). Reviewer: Juan Gerardo Alcazar (Alcala da Henares) MSC: 14M25 14Q15 14Q99 52B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
D’Andrea, Carlos; Sombra, Martín Rational parametrizations, intersection theory, and Newton polytopes. (English) Zbl 1181.14063 Emiris, Ioannis Z. (ed.) et al., Nonlinear computational geometry. Papers presented at the workshop, Minneapolis, MN, USA, May 29–June 2, 2007. Dordrecht: Springer (ISBN 978-1-4419-0998-5/hbk; 978-1-4419-0999-2/e-book). The IMA Volumes in Mathematics and its Applications 151, 35-50 (2010). MSC: 14Q05 12Y05 52B20 14C17 14T05 14M25 × Cite Format Result Cite Review PDF Full Text: DOI
Ardila, Federico; Develin, Mike Tropical hyperplane arrangements and oriented matroids. (English) Zbl 1175.52024 Math. Z. 262, No. 4, 795-816 (2009). Reviewer: Alexander Esterov (Moscow) MSC: 52B40 52C40 52C35 14T05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Speyer, David E. A matroid invariant via the \(K\)-theory of the Grassmannian. (English) Zbl 1222.14131 Adv. Math. 221, No. 3, 882-913 (2009). Reviewer: P. E. Frenkel (Budapest) MSC: 14T05 14C35 14M15 52B40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Develin, Mike; Yu, Josephine Tropical polytopes and cellular resolutions. (English) Zbl 1134.52006 Exp. Math. 16, No. 3, 277-291 (2007). MSC: 52A30 13D02 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Sturmfels, Bernd; Tevelev, Jenia; Yu, Josephine The Newton polytope of the implicit equation. (English) Zbl 1133.13026 Mosc. Math. J. 7, No. 2, 327-346 (2007). Reviewer: Alyson Reeves (Bowie) MSC: 13P10 14Q99 52B20 68W30 × Cite Format Result Cite Review PDF Full Text: arXiv
Ardila, Federico; Klivans, Caroline J. The Bergman complex of a matroid and phylogenetic trees. (English) Zbl 1082.05021 J. Comb. Theory, Ser. B 96, No. 1, 38-49 (2006). Reviewer: Kelly J. Pearson (Murray) MSC: 05B35 05C05 92D15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv