Discrete Mathematics ( IF 0.7 ) Pub Date : 2021-01-22 , DOI: 10.1016/j.disc.2020.112271 Rachel Yun Zhang
A permutation class is said to be splittable if there exist two proper subclasses such that any can be red–blue colored so that the red (respectively, blue) subsequence of is order isomorphic to an element of (respectively, ). The class is said to be composable if there exists some number of proper subclasses such that any can be written as for some . We answer a question of Karpilovskij by showing that there exists a composable permutation class that is not splittable. We also give a condition under which an infinite composable class must be splittable.
中文翻译:
排列类的可组合性和可拆分性之间的关系
排列类 如果存在两个适当的子类,则被称为可拆分的 这样任何 可以是红色-蓝色,因此红色(分别是蓝色)的子序列 对的元素是同构的 (分别, )。班级如果存在一些适当的子类,则被认为是可组合的 这样任何 可以写成 对于一些 。我们通过显示存在一个不可拆分的可组合置换类来回答Karpilovskij的问题。我们还给出了一个条件,在该条件下,无限可组合类必须是可拆分的。