7 citations · 17 across the 11 of their papers we have counts for
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Higher dimensional floorplans and Baxter d-permutations
Nicolas Bonichon, Thomas Muller, Adrian Tanasa
A dimensional mosaic floorplan is a partition of a rectangle by other rectangles with no empty rooms. These partitions (considered up to some deformations) are known to be in b…
Baxter -permutations and other pattern avoiding classes
Nicolas Bonichon, Pierre-Jean Morel
A permutation of size can be identified to its diagram in which there is exactly one point per row and column in the grid . In this paper we consider multidimensional pe…
Gallai's path decomposition in planar graphs
Alexandre Blanché, Marthe Bonamy, Nicolas Bonichon
In 1968, Gallai conjectured that the edges of any connected graph with vertices can be partitioned into paths. We show that this conjecture is true…
A bijection for essentially 3-connected toroidal maps
Nicolas Bonichon, Éric Fusy, Benjamin Lévêque
We present a bijection for toroidal maps that are essentially -connected (-connected in the periodic planar representation). Our construction actually proceeds on certain clo…
On the number of planar Eulerian orientations
Nicolas Bonichon, Mireille Bousquet-Mélou, Paul Dorbec +1
The number of planar Eulerian maps with n edges is well-known to have a simple expression. But what is the number of planar Eulerian orientations with n edges? This problem appears…
Baxter permutations and plane bipolar orientations
Nicolas Bonichon, Mireille Bousquet-Mélou, Eric Fusy
We present a simple bijection between Baxter permutations of size and plane bipolar orientations with n edges. This bijection translates several classical parameters of permuta…
Catalan's intervals and realizers of triangulations
Olivier Bernardi, Nicolas Bonichon
The Stanley lattice, Tamari lattice and Kreweras lattice are three remarkable orders defined on the set of Catalan objects of a given size. These lattices are ordered by inclusion:…