论文标题
A型和D群集变量的牛顿多面体的饱和度
Saturation of Newton polytopes of type A and D cluster variables
论文作者
论文摘要
我们研究了集群代数$ \ Mathcal {a}（σ）$ A型和D的牛顿多面体变量。集群代数的著名属性是月桂型现象：每个集群变量可以写成是在初始种子$σ$的初始种子群集中的lurent lotalmial中写成的。集群变量牛顿多面体是这些lurent多项式的牛顿多面体。我们表明，如果$σ$具有主系数或边界冷冻变量，则所有群集变量牛顿多面体都饱和。我们还表征了这些牛顿多面体为\ emph {empty};也就是说，当他们没有非vertex晶格点时。
We study Newton polytopes for cluster variables in cluster algebras $\mathcal{A}(Σ)$ of types A and D. A famous property of cluster algebras is the Laurent phenomenon: each cluster variable can be written as a Laurent polynomial in the cluster variables of the initial seed $Σ$. The cluster variable Newton polytopes are the Newton polytopes of these Laurent polynomials. We show that if $Σ$ has principal coefficients or boundary frozen variables, then all cluster variable Newton polytopes are saturated. We also characterize when these Newton polytopes are \emph{empty}; that is, when they have no non-vertex lattice points.
