Bijections for Baxter families and related objects

DOI10.1016/j.jcta.2010.03.017zbMath1238.05010arXiv0803.1546OpenAlexW2146998892WikidataQ60692215 ScholiaQ60692215MaRDI QIDQ2431261

Marc Noy, David Orden, Éric Fusy, Stefan Felsner

Publication date: 11 April 2011

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.1546

zbMATH Keywords

Catalan numbersbijectionsSchnyder woodsBaxter numbersorientations of planar maps

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Permutations, words, matrices (05A05) Enumeration in graph theory (05C30) Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (33)

Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processes ⋮ On height isotopy classes of embeddings in the plane of a Morse function of a circle ⋮ A generating tree approach to \(k\)-nonnesting partitions and permutations ⋮ Semi-Baxter and Strong-Baxter: Two Relatives of the Baxter Sequence ⋮ Cambrian Hopf algebras ⋮ On the number of planar Eulerian orientations ⋮ Bijections for Weyl chamber walks ending on an axis, using arc diagrams and Schnyder woods ⋮ The skew Brownian permuton: A new universality class for random constrained permutations ⋮ Bipolar orientations on planar maps and \(\mathrm{SLE}_{12}\) ⋮ Generic rectangulations ⋮ An upper bound for the number of rectangulations of a planar point set ⋮ Proof of Dilks' bijectivity conjecture on Baxter permutations ⋮ Inequalities associated with the Baxter numbers ⋮ Combinatorial generation via permutation languages. III: Rectangulations ⋮ Baxter permuton and Liouville quantum gravity ⋮ Bijections for generalized Tamari intervals via orientations ⋮ Schnyder decompositions for regular plane graphs and application to drawing ⋮ Pattern-avoiding inversion sequences and open partition diagrams ⋮ Orders induced by segments in floorplans and (2-14-3, 3-41-2)-avoiding permutations ⋮ Unnamed Item ⋮ The Hopf algebra of diagonal rectangulations. ⋮ A generic method for bijections between blossoming trees and planar maps ⋮ Coxeter-bicatalan combinatorics ⋮ Unnamed Item ⋮ Mixing Times of Markov Chains of 2-Orientations ⋮ Tableau sequences, open diagrams, and Baxter families ⋮ Unnamed Item ⋮ The generating function of planar Eulerian orientations ⋮ Slicings of parallelogram polyominoes: Catalan, Schröder, Baxter, and other sequences ⋮ Baxter posets ⋮ Bijective counting of plane bipolar orientations and Schnyder woods ⋮ New bijective links on planar maps via orientations ⋮ A mating-of-trees approach for graph distances in random planar maps

Uses Software

• OEIS

Cites Work

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• Strictly convex drawings of planar graphs
• Optimal coding and sampling of triangulations
• Convex drawings of 3-connected plane graphs
• Orthogonal surfaces and their CP-orders
• Intervals in Catalan lattices and realizers of triangulations
• On the number of planar orientations with prescribed degrees
• Bijective counting of plane bipolar orientations and Schnyder woods
• Binomial determinants, paths, and hook length formulae
• A unified approach to visibility representations of planar graphs
• Rectilinear planar layouts and bipolar orientations of planar graphs
• Shuffle of parenthesis systems and Baxter permutations
• Embedding planar graphs in four pages
• Planar graphs and poset dimension
• Baxter permutations rise again
• On grid intersection graphs
• The number of Baxter permutations
• Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems
• Bipolar orientations revisited
• A left-first search algorithm for planar graphs
• Stack words, standard tableaux and Baxter permutations
• Doubly alternating Baxter permutations are Catalan
• On the number of rectangulations of a planar point set
• A bijection between realizers of maximal plane graphs and pairs of non-crossing Dyck paths
• Straight-Line Drawing of Quadrangulations
• Improved Compact Visibility Representation of Planar Graph via Schnyder's Realizer
• The Order Dimension of Convex Polytopes
• Baxter permutations and plane bipolar orientations
• Baxter permutations
• On topological aspects of orientations
• Dichromatic polynomials and Potts models summed over rooted maps

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