论文标题
热带矩阵的幂的周期性瞬变的新界限：使用环状和因子等级
New bounds on the periodicity transient of the powers of a tropical matrix: using cyclicity and factor rank
论文作者
论文摘要
基于Merlet，Nowak和Sergeev在先前论文中开发的弱CSR方法的基础，我们为热带基质的权力的周期性阈值建立了新的界限。根据这种方法，最终周期性阈值的边界采用t = max的形式（T_1，T_2），其中T_1在弱的CSR扩展开始时是绑定的，而T_2在此之后绑定了第一个CSR项开始主导。 本文中建立的T_1和T_2上的新界限利用了相关图的循环性和矩阵的（热带）因子等级，在有利的情况下，矩阵的（热带）因子等级可实现大大改善。特别是对于T_1，我们获得了Schwarz，Kim和Gregory-Kirkland-Pullman的新扩展，以前称为Digraphs指数的边界。对于T_2上的类似界限，我们介绍了步行还原阈值的新颖概念，并在其上建立界限，同时使用循环和因子等级。
Building on the weak CSR approach developed in a previous paper by Merlet, Nowak and Sergeev, we establish new bounds for the periodicity threshold of the powers of a tropical matrix. According to that approach, bounds on the ultimate periodicity threshold take the form of T=max(T_1,T_2), where T_1 is a bound on the time after which the weak CSR expansion starts to hold and T_2 is a bound on the time after which the first CSR term starts to dominate. The new bounds on T_1 and T_2 established in this paper make use of the cyclicity of the associated graph and the (tropical) factor rank of the matrix, which leads to much improved bounds in favorable cases. For T_1, in particular, we obtain new extensions of bounds of Schwarz, Kim and Gregory-Kirkland-Pullman, previously known as bounds on exponents of digraphs. For similar bounds on T_2, we introduce the novel concept of walk reduction threshold and establish bounds on it that use both cyclicity and factor rank.
