Egge triples and unbalanced Wilf-equivalence

Abstract

Egge conjectured that permutations avoiding the set of patterns $\{2143,3142,\tau \}$, where $\tau \in \{246135,254613,263514,524361,546132\}$, are enumerated by the large Schröder numbers. Consequently, $\{2143,3142,\tau \}$ with $\tau$ as above is Wilf-equivalent to the set of patterns $\{2413,3142\}$. Burstein and Pantone proved the case of $\tau =246135$. We prove the remaining four cases. As a byproduct of our proof, we also enumerate the case $\tau =4132$.

20 pages, 6 figures (published version)

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