Counting colored planar maps: algebraicity results (2009)
Bernardi, Olivier, Bousquet-Mélou, Mireille
We address the enumeration of properly q-colored planar maps, or more precisely, the enumeration of rooted planar maps M weighted by their chromatic polynomial \chi_M(q) and counted by the number of...
A Bijection between well-labelled positive paths and matchings (2009)
Bernardi, Olivier, Duplantier, Bertrand, Nadeau, Philippe
A well-labelled positive path of size n is a pair (p,\sigma) made of a word p=p_1p_2...p_{n-1} on the alphabet {-1, 0,+1} such that the sum of the letters of any prefix is non-negative, together with...
Enumerating simplicial decompositions of surfaces with boundaries (2009)
Bernardi, Olivier, Rué, Juanjo
It is well-known that the triangulations of the disc with $n+2$ vertices on its boundary are counted by the $n$th Catalan number $C(n)=\frac{1}{n+1}{2n \choose n}$. This paper deals with the...
Enumerating simplicial decompositions of surfaces with boundaries (2009)
Bernardi, Olivier, Rué, Juanjo
It is well-known that the triangulations of the disc with $n+2$ vertices on its boundary are counted by the $n$th Catalan number $C(n)=\frac{1}{n+1}{2n \choose n}$. This paper deals with the...
Enumerating simplicial decompositions of surfaces with boundaries (2009)
Bernardi, Olivier, Rué, Juanjo
It is well-known that the triangulations of the disc with $n+2$ vertices on its boundary are counted by the $n$th Catalan number $C(n)=\frac{1}{n+1}{2n \choose n}$. This paper deals with the...
A Bijection between well-labelled positive paths and matchings (2009)
Bernardi, Olivier, Duplantier, Bertrand, Nadeau, Philippe
A well-labelled positive path of size n is a pair (p,\sigma) made of a word p=p_1p_2...p_{n-1} on the alphabet {-1, 0,+1} such that the sum of the letters of any prefix is non-negative, together with...
A Bijection between well-labelled positive paths and matchings (2009)
Bernardi, Olivier, Duplantier, Bertrand, Nadeau, Philippe
A well-labelled positive path of size n is a pair (p,\sigma) made of a word p=p_1p_2...p_{n-1} on the alphabet {-1, 0,+1} such that the sum of the letters of any prefix is non-negative, together with...
Counting colored planar maps: algebraicity results (2009)
Bernardi, Olivier, Bousquet-Mélou, Mireille
We address the enumeration of properly q-colored planar maps, or more precisely, the enumeration of rooted planar maps M weighted by their chromatic polynomial \chi_M(q) and counted by the number of...
Counting colored planar maps: algebraicity results (2009)
Bernardi, Olivier, Bousquet-Mélou, Mireille
We address the enumeration of properly q-colored planar maps, or more precisely, the enumeration of rooted planar maps M weighted by their chromatic polynomial \chi_M(q) and counted by the number of...
Solution to a combinatorial puzzle arising from Mayer's theory of cluster integrals (2008)
Mayer's theory of cluster integrals allows one to write the partition function of a gas model as a generating function of weighted graphs. Recently, Labelle, Leroux and Ducharme have studied the...
On the growth rate of minor-closed classes of graphs (2008)
Bernardi, Olivier, Noy, Marc, Welsh, Dominic
"Vegeu el resum a l'inici del document del fitxer adjunt."
Solution to a combinatorial puzzle arising from Mayer's theory of cluster integrals (2008)
Mayer's theory of cluster integrals allows one to write the partition function of a gas model as a generating function of weighted graphs. Recently, Labelle, Leroux and Ducharme have studied the...
Solution to a combinatorial puzzle arising from Mayer's theory of cluster integrals (2008)
Mayer's theory of cluster integrals allows one to write the partition function of a gas model as a generating function of weighted graphs. Recently, Labelle, Leroux and Ducharme have studied the...
On the growth rate of minor-closed classes of graphs (2007)
Bernardi, Olivier, Noy, Marc, Welsh, Dominic
A minor-closed class of graphs is a set of labelled graphs which is closed under isomorphism and under taking minors. For a minor-closed class $C$, we let $c_n$ be the number of graphs in $C$ which...
Catalan's intervals and realizers of triangulations (2007)
Bernardi, Olivier, Bonichon, Nicolas
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: the Stanley...
Catalan's intervals and realizers of triangulations (2007)
Bernardi, Olivier, Bonichon, Nicolas
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: the Stanley...
Catalan's intervals and realizers of triangulations (2007)
Bernardi, Olivier, Bonichon, Nicolas
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: the Stanley...
On the growth rate of minor-closed classes of graphs (2007)
Bernardi, Olivier, Noy, Marc, Welsh, Dominic
A minor-closed class of graphs is a set of labelled graphs which is closed under isomorphism and under taking minors. For a minor-closed class $C$, we let $c_n$ be the number of graphs in $C$ which...
On the growth rate of minor-closed classes of graphs (2007)
Bernardi, Olivier, Noy, Marc, Welsh, Dominic
A minor-closed class of graphs is a set of labelled graphs which is closed under isomorphism and under taking minors. For a minor-closed class $C$, we let $c_n$ be the number of graphs in $C$ which...
Catalan's intervals and realizers of triangulations (2007)
Bernardi, Olivier, Bonichon, Nicolas
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: the Stanley...
Tutte polynomial, subgraphs, orientations and sandpile model: new connections via embeddings (2006)
For any graph G with n edges, the spanning subgraphs and the orientations of G are both counted by the evaluation T_G(2,2)=2^n of its Tutte polynomial. We define a bijection $\Phi$ between spanning...
A characterization of the Tutte polynomial via combinatorial embeddings (2006)
We give a new characterization of the Tutte polynomial of graphs. Our characterization is formally close (but inequivalent) to the original definition given by Tutte as the generating function of...
A characterization of the Tutte polynomial via combinatorial embeddings (2006)
We give a new characterization of the Tutte polynomial of graphs. Our characterization is formally close (but inequivalent) to the original definition given by Tutte as the generating function of...
A characterization of the Tutte polynomial via combinatorial embeddings (2006)
We give a new characterization of the Tutte polynomial of graphs. Our characterization is formally close (but inequivalent) to the original definition given by Tutte as the generating function of...
Bijective counting of Kreweras walks and loopless triangulations (2006)
We consider lattice walks in the plane starting at the origin, remaining in the first quadrant and made of West, South and North-East steps. In 1965, Germain Kreweras discovered a remarkably simple...
Bijective counting of Kreweras walks and loopless triangulations (2006)
We consider lattice walks in the plane starting at the origin, remaining in the first quadrant and made of West, South and North-East steps. In 1965, Germain Kreweras discovered a remarkably simple...
Bijective counting of Kreweras walks and loopless triangulations (2006)
We consider lattice walks in the plane starting at the origin, remaining in the first quadrant and made of West, South and North-East steps. In 1965, Germain Kreweras discovered a remarkably simple...
Bijective counting of tree-rooted maps and shuffles of parenthesis systems (2006)
The number of tree-rooted maps, that is, rooted planar maps with a distinguished spanning tree, of size $n$ is C(n)C(n+1) where C(n)=binomial(2n,n)/(n+1) is the nth Catalan number. We present a (long...
Bijective counting of tree-rooted maps and shuffles of parenthesis systems (2006)
The number of tree-rooted maps, that is, rooted planar maps with a distinguished spanning tree, of size $n$ is C(n)C(n+1) where C(n)=binomial(2n,n)/(n+1) is the nth Catalan number. We present a (long...
On triangulations with high vertex degree (2006)
We solve three enumerative problems concerning families of planar maps. More precisely, we establish algebraic equations for the generating function of non-separable triangulations in which all...
Bijective counting of tree-rooted maps and shuffles of parenthesis systems (2006)
The number of tree-rooted maps, that is, rooted planar maps with a distinguished spanning tree, of size $n$ is C(n)C(n+1) where C(n)=binomial(2n,n)/(n+1) is the nth Catalan number. We present a (long...
On triangulations with high vertex degree (2006)
We solve three enumerative problems concerning families of planar maps. More precisely, we establish algebraic equations for the generating function of non-separable triangulations in which all...
On triangulations with high vertex degree (2006)
We solve three enumerative problems concerning families of planar maps. More precisely, we establish algebraic equations for the generating function of non-separable triangulations in which all...
A characterization of the Tutte polynomial via combinatorial embeddings (2006)
We give a new characterization of the Tutte polynomial of graphs. Our characterization is formally close (but inequivalent) to the original definition given by Tutte as the generating function of...
Bijective counting of Kreweras walks and loopless triangulations (2006)
We consider lattice walks in the plane starting at the origin, remaining in the first quadrant and made of West, South and North-East steps. In 1965, Germain Kreweras discovered a remarkably simple...
Bijective counting of tree-rooted maps and shuffles of parenthesis systems (2006)
The number of tree-rooted maps, that is, rooted planar maps with a distinguished spanning tree, of size $n$ is C(n)C(n+1) where C(n)=binomial(2n,n)/(n+1) is the nth Catalan number. We present a (long...
On triangulations with high vertex degree (2006)
We solve three enumerative problems concerning families of planar maps. More precisely, we establish algebraic equations for the generating function of non-separable triangulations in which all...
Tutte polynomial, subgraphs, orientations and sandpile model: new connections via embeddings (2006)
For any graph G with n edges, the spanning subgraphs and the orientations of G are both counted by the evaluation T_G(2,2)=2^n of its Tutte polynomial. We define a bijection $\Phi$ between spanning...
Tutte polynomial, subgraphs, orientations and sandpile model: new connections via embeddings (2006)
For any graph G with n edges, the spanning subgraphs and the orientations of G are both counted by the evaluation T_G(2,2)=2^n of its Tutte polynomial. We define a bijection $\Phi$ between spanning...
A characterization of the Tutte polynomial via combinatorial embeddings (2006)
We give a new characterization of the Tutte polynomial of graphs. Our characterization is formally close (but inequivalent) to the original definition given by Tutte as the generating function of...
Bijective counting of Kreweras walks and loopless triangulations (2006)
We consider lattice walks in the plane starting at the origin, remaining in the first quadrant and made of West, South and North-East steps. In 1965, Germain Kreweras discovered a remarkably simple...
Bijective counting of tree-rooted maps and shuffles of parenthesis systems (2006)
The number of tree-rooted maps, that is, rooted planar maps with a distinguished spanning tree, of size $n$ is C(n)C(n+1) where C(n)=binomial(2n,n)/(n+1) is the nth Catalan number. We present a (long...
On triangulations with high vertex degree (2006)
We solve three enumerative problems concerning families of planar maps. More precisely, we establish algebraic equations for the generating function of non-separable triangulations in which all...