Tropically planar graphs

具有固定j-不变量的热带与代数椭圆平面曲线

Tropical and algebraic elliptic plane curves with fixed j-invariant

该研究通过热带计数特定椭圆曲线，结合对应定理，给出代数计数的另一种证明，拓展了枚举几何的相关方法。

Tropical hyperelliptic curves in the plane

Abstractly, tropical hyperelliptic curves are metric graphs that admit a two-to-one harmonic morphism to a tree. They also appear as embedded tropical curves in the plane arising from triangulations of polygons with all interior lattice points collinear. We prove that hyperelliptic graphs can only arise from such polygons. Along the way we will prove certain graphs do not embed tropically in the plane due to entirely combinatorial obstructions, regardless of whether their metric is actually hyperelliptic.

热带秩与维数在热带有理函数的semimodule中的相等性，以及计算方面

Equality of tropical rank and dimension for semimodules of tropical rational functions, and computational aspects

本文证明了热带有理函数semimodule的热带秩等于其拓扑维数，并探讨了计算热带秩的复杂性。

有限图的热带交叉数

The tropical crossing number of a finite graph

该研究定义了有限非度量图的热带交叉数，证明存在热带交叉数为任意正整数d且图论交叉数至多为d的图，求解了最小非热带平面图的热带交叉数并证明其可随顶点数二次增长。