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.

- Journal: Discrete Math. Theor. Comput. Sci. Proc.
- arXiv: 1403.5014 [math.CO]

**The Rearrangement Conjecture:**(due to Kitaev, Liese, Remmel, and Sagan) If two words are Wilf-equivalent, then they are rearrangements of each other.**Conjecture 1.2:**If two words are Wilf-equivalent, then they are strongly Wilf-equivalent.*(Note: The resolution of this conjecture would prove the Rearrangement Conjecture by the results in this paper.)*

- Shift Equivalence in the Generalized Factor Order, by Jennifer Fidler, Daniel Glasscock, Brian Miceli, Jay Pantone, and Min Xu