# Jay Pantone

## On the Rearrangement Conjecture for Generalized Factor Order over $$\mathbb{P}$$

with Vincent Vatter

The Rearrangement Conjecture states that if two words over $$\mathbb{P}$$ are Wilf-equivalent in the factor order on $$\mathbb{P}^\ast$$ then they are rearrangements of each other. We introduce the notion of strong Wilf-equivalence and prove that if two words over $$\mathbb{P}$$ are strongly Wilf-equivalent then they are rearrangements of each other. We further conjecture that Wilf-equivalence implies strong Wilf-equivalence.