Pattern avoidance and the fundamental bijection
Pattern avoidance and the fundamental bijection
The fundamental bijection is a bijection $\theta:\mathcal{S}_n\to\mathcal{S}_n$ in which one uses the standard cycle form of one permutation to obtain another permutation in one-line form. In this paper, we enumerate the set of permutations $\pi \in \mathcal{S}_n$ that avoids a pattern $\sigma \in \mathcal{S}_3$, whose image $\theta(\pi)$ also avoids $\sigma$. …