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arXiv · 1902.02705

Combinatorial specifications for juxtapositions of permutation classes

Robert Brignall·Jakub Sliacan
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Abstract

We show that, given a suitable combinatorial specification for a permutation class $\mathcal{C}$, one can obtain a specification for the juxtaposition (on either side) of $\mathcal{C}$ with Av(21) or Av(12), and that if the enumeration for $\mathcal{C}$ is given by a rational or algebraic generating function, so is the enumeration for the juxtaposition. Furthermore this process can be iterated, thereby providing an effective method to enumerate any 'skinny' $k\times 1$ grid class in which at most one cell is non-monotone, with a guarantee on the nature of the enumeration given the nature of the enumeration of the non-monotone cell.

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Robert Brignall, Jakub Sliacan. 2019-02-07. Combinatorial specifications for juxtapositions of permutation classes. https://arxiv.org/abs/1902.02705

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