论文标题
KAC多项式的渐近行为
Asymptotic behaviour of Kac polynomials
论文作者
论文摘要
我们猜想了一个由计算支持的公式，以估算箭量的KAC多项式，该公式仅取决于每个顶点的环数。在增加箭头数时，我们证明了颤抖的重新归一化的KAC多项式的收敛性：它们在功率序列中收敛，并具有线性收敛速率。然后，我们提出了一个关于KAC多项式系数的全局行为的猜想。所有计算均使用SageMath进行。
We conjecture a formula supported by computations for the valuation of Kac polynomials of a quiver, which only depends on the number of loops at each vertex. We prove a convergence property of renormalized Kac polynomials of quivers when increasing the number of arrows: they converge in the ring of power series, with a linear rate of convergence. Then, we propose a conjecture concerning the global behaviour of the coefficients of Kac polynomials. All computations were made using SageMath.
