Now showing items 1-20 of 35

• #### A solution to the tennis ball problem ﻿

(2005)
Article
Open Access
We present a complete solution to the so-called tennis ball problem, which is equivalent to counting the number of lattice paths in the plane that use North and East steps and lie between certain boundaries. The solution ...
• #### Bijections for Baxter families and related objects ﻿

(2011-04)
Article
Open Access
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 ...
• #### CÀLCUL EN UNA VARIABLE ﻿

(Universitat Politècnica de Catalunya, 2021-01-12)
Exam
• #### CÀLCUL EN UNA VARIABLE ﻿

(Universitat Politècnica de Catalunya, 2020-10-26)
Exam
• #### CÀLCUL EN UNA VARIABLE | (Examen extraordinari) ﻿

(Universitat Politècnica de Catalunya, 2019-07-01)
Exam
• #### Combinatòria : Problemes ﻿

(Universitat Politècnica de Catalunya, 1997)
Lecture notes
Open Access
• #### Combinatòria : Problemes ﻿

(Universitat Politècnica de Catalunya, 1997)
Lecture notes
Open Access
• #### Counting outerplanar maps ﻿

(2017-04-13)
Article
Open Access
A map is outerplanar if all its vertices lie in the outer face. We enumerate various classes of rooted outerplanar maps with respect to the number of edges and vertices. The proofs involve several bijections with lattice ...
• #### Counting polygon dissections in the projective plane ﻿

(2008-10)
Article
Open Access
For each value of k ≥ 2, we determine the number pn of ways of dissecting a polygon in the projective plane into n subpolygons with k + 1 sides each. In particular, if k = 2 we recover a result of Edelman and Reiner (1997) ...
• #### Cycles of given lengths in unicyclic components in sparse random graphs ﻿

(Elsevier, 2021-04-01)
Article
Open Access
Let L be subset of {3,4,…} and let Xn,M(L) be the number of cycles belonging to unicyclic components whose length is in L in the random graph G(n,M). We find the limiting distribution of Xn,M(L) in the subcritical regime ...
• #### Disecciones de un polígono en el plano proyectivo ﻿

Conference lecture
Restricted access - publisher's policy
En este trabajo obtenemos expresiones explícitas de las funciones generadoras de las triangulaciones y cuadrangulaciones del espacio topológico correspondiente a la supresión de un n-ágono del plano proyectivo real. En el ...
• #### Enumeration of labeled 4-regular planar graphs ﻿

(2017-08-01)
Article
Open Access
In this extended abstract, we present the first combinatorial scheme for counting labeled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function ...
• #### Enumeration of labelled 4-regular planar graphs ﻿

(2019-08-01)
Article
Open Access
We present the first combinatorial scheme for counting labelled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function of labelled 4-regular ...
• #### Further results on random cubic planar graphs ﻿

(2020-06)
Article
Open Access
We provide precise asymptotic estimates for the number of several classes of labeled cubic planar graphs, and we analyze properties of such random graphs under the uniform distribution. This model was first analyzed by ...
• #### Geometric tree graphs of points in convex position ﻿

(1997)
Article
Open Access
Given a set $P$ of points in the plane, the geometric tree graph of $P$ is defined as the graph $T(P)$ whose vertices are non-crossing rectilinear spanning trees of $P$, and where two trees $T_1$ and $T_2$ are adjacent ...
• #### Graph classes with given 3-connected components: asymptotic counting, limit laws and critical phenomena ﻿

(Edicions de la Universitat de Lleida (UdL), 2008)
Conference lecture
Restricted access - publisher's policy
Consider a family T of 3-connected graphs, and let G be the class of graphs whose 3-connected components are graphs in T . We present a general framework for analyzing such graphs classes based on singularity analysis of ...
• #### Graphs of non-crossing perfect matchings ﻿

(2001)
Article
Open Access
Let Pn be a set of n = 2m points that are the vertices of a convex polygon, and let Mm be the graph having as vertices all the perfect matchings in the point set Pn whose edges are straight line segments and do not cross, ...
• #### Identities for non-crossing graphs and multigraphs ﻿

(2008-12)
Article
Restricted access - publisher's policy
We refine an identity between the numbers of certain non-crossing graphs and multigraphs, by modifying a bijection found by P. Podbrdský [A bijective proof of an identity for noncrossing graphs, Discrete Math. 260 (2003) ...
• #### Isolated cycles of critical random graphs ﻿

(Society for Industrial and Applied Mathematics (SIAM), 2017)
Conference report
Open Access
Consider the Erdos-Renyi random graph G(n, M) built with n vertices and M edges uniformly randomly chosen from the set of n2 edges. Let L be a set of positive integers. For any number of edges M 6n/2 + O(n 2/3 ), we compute ...
• #### Limiting probabilities of first order properties of random sparse graphs and hypergraphs ﻿

(2021-08-18)
Article
Open Access
Let Gn be the binomial random graph G(n, p = c/n) in the sparse regime, which as is well-known undergoes a phase transition at c = 1. Lynch (Random Structures Algorithms, 1992) showed that for every first order sentence ...