Jay Pantone

Universal Layered Permutations

with Michael Albert, Michael Engen, and Vince Vatter

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

• 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.