Bijections for Baxter families and related objects

Autor: íric Fusy, Marc Noy, Stefan Felsner, David Orden

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
Journal of Combinatorial Theory, Series A
Journal of Combinatorial Theory, Series A, Elsevier, 2011, 118 (3), pp.993-1020. ⟨10.1016/j.jcta.2010.03.017⟩
Journal of Combinatorial Theory, Series A, 2011, 118 (3), pp.993-1020. ⟨10.1016/j.jcta.2010.03.017⟩
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

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

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5c67e228423df691001b377c5d2fb34d

Bijective counting of plane bipolar orientations and Schnyder woods

Autor: Gilles Schaeffer, íric Fusy, Dominique Poulalhon

Publikováno v: European Journal of Combinatorics. 30(7):1646-1658

A bijection $\Phi$ is presented between plane bipolar orientations with prescribed numbers of vertices and faces, and non-intersecting triples of upright lattice paths with prescribed extremities. This yields a combinatorial proof of the following fo

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A simple model of trees for unicellular maps

Autor: Valentin Féray, íric Fusy, Guillaume Chapuy

Publikováno v: Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics and Theoretical Computer Science (DMTCS)
24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), 2012, Nagoya, Japan. pp.215-226
Journal of Combinatorial Theory, Series A
Journal of Combinatorial Theory, Series A, Elsevier, 2013, 120 (8), pp.Pages 2064-2092. ⟨10.1016/j.jcta.2013.08.003⟩
Journal of Combinatorial Theory, Series A, 2013, 120 (8), pp.Pages 2064-2092. ⟨10.1016/j.jcta.2013.08.003⟩
Scopus-Elsevier

We consider unicellular maps, or polygon gluings, of fixed genus. A few years ago the first author gave a recursive bijection transforming unicellular maps into trees, explaining the presence of Catalan numbers in counting formulas for these objects.

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http://arxiv.org/abs/1202.3252

Unified bijections for maps with prescribed degrees and girth

Autor: íric Fusy, Olivier Bernardi

Publikováno v: Journal of Combinatorial Theory, Series A
Journal of Combinatorial Theory, Series A, 2012, 119, pp.1351-1387

International audience; This article presents unified bijective constructions for planar maps, with control on the face degrees and on the girth. Recall that the girth is the length of the smallest cycle, so that maps of girth at least $d=1,2,3$ are

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http://arxiv.org/abs/1102.3619

Transversal structures on triangulations: a combinatorial study and straight-line drawings

Autor: íric Fusy

This article focuses on a combinatorial structure specific to triangulated plane graphs with quadrangular outer face and no separating triangle, which are called irreducible triangulations. The structure has been introduced by Xin He under the name o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ecf4ad5ae14043d21cadf40177f4e138