# AARON

Refined restricted permutations. Derangements (and more generally the notion of ”fixed points of a permutation”) are concepts related to the cycle-structre, i.e. two-line notation, i.e. permutations qua 1-1 functions from [1,n] to [1,n]. On the other hand, Pattern-avoidance (and Wilf- equivalence) are inherently ”wordy”, i.e. pertain to permutations qua words. Perhaps this is why no one noticed the amazing and easily-stated fact that the number of 132-avoiding derangements equals the number of 321-avoiding derangements, and even more amazingly, that the same is true if you replace ”derangement” by ”with i fixed points”, for ANY $i$ between $0$ and $n$. This astounding fact was first discovered emprically by Aaron Robertson ...

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## References in zbMATH (referenced in 18 articles , 1 standard article )

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