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The relation between composability and splittability of permutation classes
Discrete Mathematics ( IF 0.7 ) Pub Date : 2021-01-22 , DOI: 10.1016/j.disc.2020.112271
Rachel Yun Zhang

A permutation class C is said to be splittable if there exist two proper subclasses A,BC such that any σC can be red–blue colored so that the red (respectively, blue) subsequence of σ is order isomorphic to an element of A (respectively, B). The class C is said to be composable if there exists some number of proper subclasses A1,,AkC such that any σC can be written as α1αk for some αiAi. 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 C如果存在两个适当的子类,则被称为可拆分的一种C 这样任何 σC 可以是红色-蓝色,因此红色(分别是蓝色)的子序列 σ 对的元素是同构的 一种 (分别, )。班级C如果存在一些适当的子类,则被认为是可组合的一种1个一种ķC 这样任何 σC 可以写成 α1个αķ 对于一些 α一世一种一世。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。

更新日期:2021-01-24
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