标题： 无限连通系统中的假花 显示英文标题

标题： Pseudoflowers in infinite connectivity systems

摘要： 给定一个图或拟阵，tangles 的树是一个树分解，它展示了连通性的结构：分解树的每条边都会产生一个分离，即一种将图或拟阵分成两部分的方式；对于每个位于某些分离不同侧的高连通区域（用 tangles 编码），某个由边产生的分离可以区分它们。 由 tangles 树产生的分离不会交叉。 一种显示更多连通性结构的方法是向 tangles 树中插入更多的结构，例如 Oxley、Semple 和 Whittle 在 2007 年为拟阵引入的花朵，并由 Clark 和 Whittle 在 2013 年推广到有限连通系统。 花朵所显示的大多数分离都是交叉的。 为了将这一理论扩展到无限情况，我们将花朵的概念推广到无限连通系统，并证明存在极大广义花朵。 此外，我们在无限拟阵的特殊情况下证明，两种类型的花朵（海葵和雏菊）只有海葵可以扩展为真正的无限对象，并为一般的连通系统提供了无限雏菊存在的条件描述。 此外，我们还从更抽象的角度描述了 tangles 和区分它们的分离之间的相互作用，这在其他方面提供了为什么存在极大广义花朵的额外动机。 显示英文摘要

摘要： Given a graph or a matroid, a tree of tangles is a tree decomposition that displays the structure of the connectivity: every edge of the decomposition tree induces a separation, that is, a way to divide the graph or matroid into two parts; and for every two highly connected areas (encoded as tangles) that live on different sides of some separation, some separation induced by an edge distinguishes them. Separations induced by a tree of tangles cannot cross. One approach to display even more connectivity structure is to insert even more structure into a tree of tangles, for example the flowers that were introduced by Oxley, Semple and Whittle in 2007 for matroids and generalised to finite connectivity systems by Clark and Whittle in 2013. Most of the separations displayed by a flower are crossing. In order to extend this theory to the infinite case, we generalise the notion of flowers to infinite connectivity systems, and show that there are maximal generalised flowers. Also, we show in the special case of infinite matroids that of the two types of flowers (anemones and daisies) only anemones can be extended to truly infinite objects, and provide for general connectivity systems a characterisation of when infinite daisies exist. Furthermore we describe a more abstract view on the interaction of tangles and separations distinguishing them, which among other things provides additional motivation for why there should be maximal generalised flowers.