Now showing items 1-20 of 46

• #### 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, 2020-10-26)
Exam
• #### CÀLCUL EN UNA VARIABLE  ﻿

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

(Universitat Politècnica de Catalunya, 2019-07-01)
Exam
• #### CÀLCUL EN UNA VARIABLE | EXTRAORDINARI ﻿

(Universitat Politècnica de Catalunya, 2023-06-28)
Exam
• #### CÀLCUL EN UNA VARIABLE | FINAL  ﻿

(Universitat Politècnica de Catalunya, 2022-01-17)
Exam
• #### CÀLCUL EN UNA VARIABLE | FINAL  ﻿

(Universitat Politècnica de Catalunya, 2023-01-19)
Exam
• #### CÀLCUL EN UNA VARIABLE | PARCIAL ﻿

(Universitat Politècnica de Catalunya, 2021-11-02)
Exam
• #### Chordal graphs with bounded tree-width ﻿

(Masaryk University, 2023)
Conference lecture
Open Access
Given $t\ge 2$ and $0\le k\le t$, we prove that the number of labelled $k$-connected chordal graphs with $n$ vertices and tree-width at most $t$ is asymptotically $c n^{-5/2} \gamma^n n!$, as $n\to\infty$, for some constants ...
• #### 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 chordal planar graphs and maps ﻿

(2023-01-01)
Article
Open Access
We determine the number of labelled chordal planar graphs with n vertices, which is asymptotically for a constant and . We also determine the number of rooted simple chordal planar maps with n edges, which is asymptotically ...
• #### 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 ...
• #### Enumeration of labelled 4-regular planar graphs II: asymptotics ﻿

(2023-05)
Article
Open Access
This work is a follow-up of the article (Noy et al., 2019), where the authors solved the problem of counting labelled 4-regular planar graphs. In this paper, we obtain a precise asymptotic estimate for the number of labelled ...