# Jay Pantone

## Two Examples of Unbalanced Wilf-Equivalence

with Alex Burstein

We prove that the set of patterns $$\{1324,3416725\}$$ is Wilf-equivalent to the pattern $$1234$$ and that the set of patterns $$\{2143,3142,246135\}$$ is Wilf-equivalent to the set of patterns $$\{2413,3142\}$$. These are the first known unbalanced Wilf-equivalences for classical patterns between finite sets of patterns.

• Conjecture 3.1: The classes $$\text{Av}(2413)$$ and $$\text{Av}(2143,246135)$$ are Wilf-equivalent.
• Conjecture: (due to Eric Egge) The class $$\text{Av}(2413,3142)$$ is Wilf-equivalent to the class $$\text{Av}(2143, 3142, \beta)$$ for any $$\beta \in \{246135,$$$$254613, 263514, 362415, 461325, 524361, 546132, 614352\}$$.