Permutree sorting

07/15/2020

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by   Vincent Pilaud, et al.

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Generalizing stack sorting and c-sorting for permutations, we define the permutree sorting algorithm. Given two disjoint subsets U and D of {2, …, n-1}, the (U,D)-permutree sorting tries to sort the permutation π∈𝔖_n and fails if and only if there are 1 ≤ i < j < k ≤ n such that π contains the subword jki if j ∈ U and kij if j ∈ D. This algorithm is seen as a way to explore an automaton which either rejects all reduced expressions of π, or accepts those reduced expressions for π whose prefixes are all (U,D)-permutree sortable.