Refined powered-Catalan conjecture for 23-1-4-avoiding permutations

For n1n\geq 1, let AVn(23-1-4)AV_n(23\text{-}1\text{-}4) be the permutations of length nn avoiding the generalized pattern 23-1-423\text{-}1\text{-}4, and let kk be the number of right-to-left minima. Let cn,kc_{n,k} be the numbers defined by the recurrence in Equation. Refined powered-Catalan conjecture. The number of permutations in AVn(23-1-4)AV_n(23\text{-}1\text{-}4) with kk right-to-left minima is cn,kc_{n,k}. This refines the preceding equinumerosity conjecture by predicting the distribution according to right-to-left minima, but the source does not state whether it has been resolved.

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Primary source

Nicholas R. Beaton, Mathilde Bouvel, Veronica Guerrini and Simone Rinaldi, “Enumerating five families of pattern-avoiding inversion sequences; and introducing the powered Catalan numbers”, arXiv:1808.04114 (2018).

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