论文标题
pansiot-type子字复杂性定理，用于自由组的自动形态学
A Pansiot-type subword complexity theorem for automorphisms of free groups
论文作者
论文摘要
受Pansiot在替代方面的工作的启发，我们证明了有限级自由F的自由形态的类似定理：如果右无限单词X代表F的f的引人入胜的固定点，则X的子单词复杂性等于n，N，N log log n，N log N，N log N，N log N，或N^2。该证明使用组合论证的类似物和火车轨道。我们还定义了X的复发性复杂性，并将其应用于层压。特别是，我们表明，吸引层压的复杂性等效于n，n log log n，n log n或n^2（如果自动形态完全不可修复）。
Inspired by Pansiot's work on substitutions, we prove a similar theorem for automorphisms of a free group F of finite rank: if a right-infinite word X represents an attracting fixed point of an automorphism of F, the subword complexity of X is equivalent to n, n log log n, n log n, or n^2. The proof uses combinatorial arguments analogue to Pansiot's as well as train tracks. We also define the recurrence complexity of X, and we apply it to laminations. In particular, we show that attracting laminations have complexity equivalent to n, n log log n, n log n, or n^2 (to n if the automorphism is fully irreducible).
