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arXiv · 2312.11738

Labelled well-quasi-order in juxtapositions of permutation classes

Robert Brignall
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Abstract

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 $\C$ and $\DDD$ 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.

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Robert Brignall. 2023-12-18. Labelled well-quasi-order in juxtapositions of permutation classes. https://arxiv.org/abs/2312.11738

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