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- W3022016082 abstract "In this extended abstract, we investigate bijections on various classes of set partitions of classical types that preserve openers and closers. On the one hand we present bijections for types $B$ and $C$ that interchange crossings and nestings, which generalize a construction by Kasraoui and Zeng for type $A$. On the other hand we generalize a bijection to type $B$ and $C$ that interchanges the cardinality of a maximal crossing with the cardinality of a maximal nesting, as given by Chen, Deng, Du, Stanley and Yan for type $A$. For type $D$, we were only able to construct a bijection between non-crossing and non-nesting set partitions. For all classical types we show that the set of openers and the set of closers determine a non-crossing or non-nesting set partition essentially uniquely. Dans ce résumé, nous étudions des bijections entre diverses classes de partitions d'ensemble de types classiques qui préservent les openers'' et les closers''. D'une part, nous présentons des bijections pour les types $B$ et $C$ qui échangent croisées et emboôtées, qui généralisent une construction de Kasraoui et Zeng pour le type $A$. D'autre part, nous généralisons une bijection pour le type $B$ et $C$ qui échange la cardinalité d'un croisement maximal avec la cardinalité d'un emboîtement maximal comme il a été fait par Chen, Deng, Du, Stanley et Yan pour le type $A$. Pour le type $D$, nous avons seulement construit une bijection entre les partitions non croisées et non emboîtées. Pour tout les types classiques, nous montrons que l'ensemble des openers'' et l'ensemble des closers'' déterminent une partition non croisées ou non emboîtées essentiellement de façon unique." @default.
- W3022016082 created "2020-05-13" @default.
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- W3022016082 date "2010-01-01" @default.
- W3022016082 modified "2023-09-25" @default.
- W3022016082 title "Crossings and nestings in set partitions of classical types" @default.
- W3022016082 doi "https://doi.org/10.46298/dmtcs.2826" @default.
- W3022016082 hasPublicationYear "2010" @default.
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