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.

- Journal: J. Combin.
- arXiv: 1402.3842 [math.CO]

The authors would like to thank Miklós Bóna for his close reading of the paper, helpful comments in clarifying the exposition, and pointing out the connection of this paper to [4].

**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 \(\beta \in \{246135, \)\(254613, 263514, 362415, 461325, 524361, 546132, 614352\}\).*This was proved by Bloom and Burstein.*