Publication at Faculty of Mathematics and Physics |
2017
Abstract
A permutation class CC is splittable if it is contained in a merge of two of its proper subclasses, and it is 1-amalgamable if given two permutations σ and τ in C, each with a marked element, we can find a permutation π in C containing both σ and τ such that the two marked elements coincide. It was previously shown that unsplittability implies 1-amalgamability.
We prove that unsplittability and 1-amalgamability are not equivalent properties of permutation classes by showing that the class Av(1423,1342). Av(1423,1342) is both splittable and 1-amalgamable.
Our construction is based on the concept of LR-inflations, which we introduce here and which may be of independent interest.