The Preisach graph and longest increasing subsequences
Annales de l’Institut Henri Poincaré D, Tome 9 (2022) no. 4, pp. 643-657.
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The Preisach graph is a directed graph associated with a permutation ρ∈𝒮 N . We give an explicit bijection between its vertices and increasing subsequences of ρ with the property that the length of a subsequence is equal to the degree of nesting of the corresponding vertex inside a hierarchy of cycles and sub-cycles of the graph. As a consequence, the nesting degree of the Preisach graph equals the length of the longest increasing subsequence.

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DOI : 10.4171/aihpd/151
Classification : 05-XX, 82-XX
Mots-clés : Permutations, longest increasing subsequence, graphs 
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     title = {The {Preisach} graph and longest increasing subsequences},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {643--657},
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Ferrari, Patrik L.; Mungan, Muhittin; Terzi, M. Mert. The Preisach graph and longest increasing subsequences. Annales de l’Institut Henri Poincaré D, Tome 9 (2022) no. 4, pp. 643-657. doi : 10.4171/aihpd/151. http://www.numdam.org/articles/10.4171/aihpd/151/

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