We establish an exact formula for the length of the shortest permutation containing all layered permutations of length n, proving a conjecture of Gray.

- arXiv: 1710.04240 [math.CO]

**Conjecture 3:**For all \(n\), among the shortest permutations that are \(n\)-universal for the class of 321-avoiding permutations there is at least one that avoids 321 itself.