论文标题
（彩色）仿射半群中的凸度
Convexity in (colored) affine semigroups
论文作者
论文摘要
在本文中，我们探讨了Helly，Tverberg和Caratheodory的凸几何定理的仿射半群版。此外，我们开发了一种新的彩色仿射半群的理论，其中半群的发电机每个都会收到一种颜色，并且半群的要素考虑了所用的颜色（仿射半群的经典理论与所有发生器具有相同颜色的情况相吻合）。我们证明了Tverberg定理的类似物和五颜六色的Helly的Semigroups定理，以及彩色Caratheodory的Coners定理的版本。我们还证明，通过引入Frobenius编号的彩色版本，彩色的数字半群特别丰富。
In this paper, we explore affine semigroup versions of the convex geometry theorems of Helly, Tverberg, and Caratheodory. Additionally, we develop a new theory of colored affine semigroups, where the semigroup generators each receive a color and the elements of the semigroup take into account the colors used (the classical theory of affine semigroups coincides with the case in which all generators have the same color). We prove an analog of Tverberg's theorem and colorful Helly's theorem for semigroups, as well as a version of colorful Caratheodory's theorem for cones. We also demonstrate that colored numerical semigroups are particularly rich by introducing a colored version of the Frobenius number.
