Labelled well-quasi-order in juxtapositions of permutation classes

Robert Brignall¹

¹Open University UK

The electronic journal of combinatorics, Tome 31 (2024) no. 2

Résumé

The juxtaposition of permutation classes $\mathcal{C}$ and $\mathcal{D}$ is the class of all permutations formed by concatenations $\sigma\tau$, such that $\sigma$ is order isomorphic to a permutation in $\mathcal{C}$, and $\tau$ to a permutation in $\mathcal{D}$. We give simple necessary and sufficient conditions on the classes $\mathcal{C}$ and $\mathcal{D}$ for their juxtaposition to be labelled well-quasi-ordered (lwqo): namely that both $\mathcal{C}$ and $\mathcal{D}$ must themselves be lwqo, and at most one of $\mathcal{C}$ or $\mathcal{D}$ can contain arbitrarily long zigzag permutations. We also show that every class without long zigzag permutations has a growth rate which must be integral.

Détail

DOI : 10.37236/12655

Classification : 05A05, 06A07
Mots-clés : zigzag permutation, labelled well-quasi-ordering