Séminaire Lotharingien de Combinatoire, 85B.31 (2021), 12 pp.

Vincent Pilaud, Viviane Pons and Daniel Tamayo Jiménez

Permutree Sorting

Abstract. 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 a permutation π ∈ Sn and fails if and only if there are 1 ≤ i < j < kn such that π contains the subword jki with jU or kij with jD. This algorithm is seen as a way to explore an automaton which either rejects all reduced words of π, or accepts those reduced words for π whose prefixes are all (U,D)-permutree sortable.


Received: December 1, 2020. Accepted: March 1, 2021. Final version: April 29, 2021.

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