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Citació: Felsner, S. [et al.]. Bijections for Baxter families and related objects. "Journal of combinatorial theory. Series A", Abril 2011, vol. 118, núm. 3, p. 993-1020.
Títol: Bijections for Baxter families and related objects
Autor: Felsner, Stefan; Fusy, Éric; Noy Serrano, Marcos Veure Producció científica UPC; Orden, David
Data: abr-2011
Tipus de document: Article
Resum: The Baxter number can be written as $B_n = \sum_0^n \Theta_{k,n-k-1}$. These numbers have first appeared in the enumeration of so-called Baxter permutations; $B_n$ is the number of Baxter permutations of size $n$, and $\Theta_{k,l}$ is the number of Baxter permutations with $k$ descents and $l$ rises. With a series of bijections we identify several families of combinatorial objects counted by the numbers $\Theta_{k,l}$. Apart from Baxter permutations, these include plane bipolar orientations with $k+2$ vertices and $l+2$ faces, 2-orientations of planar quadrangulations with $k+2$ white and $l+2$ black vertices, certain pairs of binary trees with $k+1$ left and $l+1$ right leaves, and a family of triples of non-intersecting lattice paths. This last family allows us to determine the value of $\Theta_{k,l}$ as an application of the lemma of Gessel and Viennot. The approach also allows us to count certain other subfamilies, e.g., alternating Baxter permutations, objects with symmetries and, via a bijection with a class of plan bipolar orientations also Schnyder woods of triangulations, which are known to be in bijection with 3-orientations.
ISSN: 0097-3165
URI: http://hdl.handle.net/2117/12212
DOI: 10.1016/j.jcta.2010.03.017
Versió de l'editor: linkinghub.elsevier.com/retrieve/pii/S0097316510000671
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