A new class of multiset Wilf equivalent pairs (Q2455577)

Let \(M\) be a multiset. A pair of patterns \((\sigma,\tau)\) is called multiset Wilf equivalent if, for any \(M\), the number of permutations of \(M\) that avoid \(\sigma\) is equal to the number of permutations of \(M\) that avoid \(\tau\). In this paper the author shows that if \(\sigma_{n-2}\) is a permutation of \(\{1^{x_1}, 2^{x_2},\dots, (n-2)^{x_{n-2}}\}\) for \(n\geq 3\), then the pair \((\sigma_{n-2}(n-1)n, \sigma_{n-2}n(n- 1))\) is multiset Wilf equivalent.