The three-dimensional (3D) geological voxel model is essential for numerical simulation and
resource calculation. However, it can be challenging due to the point in polygon test in 3D …

We introduce the notion of the second lattice width of a lattice polygon and use this to
classify lattice triangles by their width and second width. This is equivalent to classifying …

This paper is dedicated to a lattice analog to the classical``sum of interior angles of a
polygon theorem''. In 2008, the first formula expressing conditions on the geometric …

We study tropically planar graphs, which are the graphs that appear in smooth tropical plane
curves. We develop necessary conditions for graphs to be tropically planar, and compute the …

Characterization of tropical plane curves up to genus six | Archiv der Mathematik Skip to main
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Given a lattice polygon P with g interior lattice points, we can associate to PP two moduli
spaces: the moduli space of algebraic curves that are non-degenerate with respect to PP …

Any smooth tropical plane curve contains a distinguished trivalent graph called its skeleton.
In 2020 Morrison and Tewari proved that the so-called big-face graphs cannot be the skeleta …

Tropical plane curves are one of the building blocks in the study of tropical algebraic
geometry. A lot of work has been done to understand and establish connections between …