Egge conjectured that permutations avoiding the set of patterns \(\{2143,3142,\tau\}\), where \(\tau\in\{246135,254613,524361,546132,263514\}\), are enumerated by the large Schroder numbers (and thus \(\{2143,3142,\tau\}\) 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 \(\tau=4132\).
Published: Australas. J. Combin., 64(1), 232-251, 2016, arXiv.