Tropical geometry of Rado matroids

被引：0
作者：
Buchanan, Calum [1 ]
Danner, Richard [1 ]
机构：
[1] Univ Vermont, Dept Math & Stat, Burlington, VT 05401 USA
来源：
DISCRETE MATHEMATICS LETTERS | 2024年 / 14卷
关键词：
tropical geometry; Chow ring; Rado matroid;
D O I：
10.47443/dml.2024.044
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we characterize the products of simplicial generators for the Chow ring of a loopless matroid, extending a result of Backman, Eur, and Simpson [J. Eur. Math. Soc., DOI: 10.4171/JEMS/1350]. We prove that the stable intersection of a collection of tropical hyperplanes centered at the origin with the Bergman fan of a matroid is the Bergman fan of the dual of a certain Rado matroid.
引用
收藏
页码：27 / 30
页数：4
相关论文
共 50 条
  • [41] An Asymptotic Comparison of Differentiable Dynamics and Tropical Geometry
    Tsuyoshi Kato
    Mathematical Physics, Analysis and Geometry, 2011, 14 : 39 - 82
  • [42] On the Decision Boundaries of Neural Networks: A Tropical Geometry Perspective
    Alfarra, Motasem
    Bibi, Adel
    Hammoud, Hasan
    Gaafar, Mohamed
    Ghanem, Bernard
    IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2023, 45 (04) : 5027 - 5037
  • [43] Max-convolution through numerics and tropical geometry
    Brysiewicz, Taylor
    Hauenstein, Jonathan D.
    Hills, Caroline
    NUMERICAL ALGORITHMS, 2024, 96 (02) : 845 - 877
  • [44] Max-convolution through numerics and tropical geometry
    Taylor Brysiewicz
    Jonathan D. Hauenstein
    Caroline Hills
    Numerical Algorithms, 2024, 96 : 845 - 877
  • [45] Khovanskii Bases, Higher Rank Valuations, and Tropical Geometry
    Kaveh, Kiumars
    Manon, Christopher
    SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY, 2019, 3 (02) : 292 - 336
  • [46] Mirror symmetry for P2 and tropical geometry
    Gross, Mark
    ADVANCES IN MATHEMATICS, 2010, 224 (01) : 169 - 245
  • [47] Kernels in tropical geometry and a Jordan-Holder theorem
    Perri, Tal
    Rowen, Louis H.
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2018, 17 (04)
  • [48] Kontsevich's formula and the WDVV equations in tropical geometry
    Gathmann, Andreas
    Markwig, Hannah
    ADVANCES IN MATHEMATICS, 2008, 217 (02) : 537 - 560
  • [49] Enumeration of complex and real surfaces via tropical geometry
    Markwig, Hannah
    Markwig, Thomas
    Shustin, Eugenii
    ADVANCES IN GEOMETRY, 2018, 18 (01) : 69 - 100
  • [50] Tropical Mathematics, Idempotent Analysis, Classical Mechanics and Geometry
    Litvinov, G. L.
    SPECTRAL THEORY AND GEOMETRIC ANALYSIS, 2011, 535 : 159 - 186
12345