Simple permutations: decidability and unavoidable substructures

大且无限2-边连通图中的不可避免子结构

Unavoidable substructures in large and infinite $2$-edge-connected graphs

本文研究了大且无限2-边连通图中的不可避免诱导子结构，发现'pinched super-clean ladders'等结构在其中扮演关键角色，并推导出关于大子图、拓扑Minor、Minor、诱导拓扑Minor、诱导Minor及欧拉子图的相关结论。

An algorithm for deciding the finiteness of the number of simple permutations in permutation classes

In this article, we describe an algorithm to determine whether a permutation class C given by a finite basis B of excluded patterns contains a finite number of simple permutations. This is a continuation of the work initiated in [Brignall, Ruskuc, Vatter, Simple permutations: decidability and unavoidable substructures, 2008], and shares several aspects with it. Like in this article, the main difficulty is to decide whether C contains a finite number of proper pin-permutations, and this decision problem is solved using automata theory. Moreover, we use an encoding of proper pin-permutations by …