Permutree sorting

Vincent Pilaud (1, 2) , Viviane Pons (3) , Daniel Tamayo Jiménez (3)

1 CNRS - Centre National de la Recherche Scientifique
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 GALaC - Graphes, Algorithmes et Combinatoire - LISN

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 < k ≤ n such that π contains the subword jki with j ∈ U or kij with j ∈ D. 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.

Mots clés: stack sorting; automata; permutrees; weak order

Domaines: Combinatoire [math.CO]

Vincent Pilaud, Viviane Pons, Daniel Tamayo Jiménez. Permutree sorting. FPSAC 2021 - 33rd International Conference on Formal Power Series and Algebraic Combinatorics, Jan 2022, Ramat Gan, Israel. pp.#31. ⟨hal-03451389⟩