Browsing by Author "Noy Serrano, Marcos"
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A solution to the tennis ball problem
Mier Vinué, Anna de; Noy Serrano, Marcos (2005)
Article
Open AccessWe present a complete solution to the socalled 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
Felsner, Stefan; Fusy, Éric; Noy Serrano, Marcos; Orden, David (201104)
Article
Open AccessThe Baxter number can be written as $B_n = \sum_0^n \Theta_{k,nk1}$. These numbers have first appeared in the enumeration of socalled Baxter permutations; $B_n$ is the number of Baxter permutations of size $n$, and ... 
CÀLCUL EN UNA VARIABLE
Noy Serrano, Marcos (Universitat Politècnica de Catalunya, 20210112)
Exam
Restricted access to the UPC academic community 
CÀLCUL EN UNA VARIABLE
Noy Serrano, Marcos (Universitat Politècnica de Catalunya, 20201026)
Exam
Restricted access to the UPC academic community 
CÀLCUL EN UNA VARIABLE  (Examen extraordinari)
Noy Serrano, Marcos (Universitat Politècnica de Catalunya, 20190701)
Exam
Restricted access to the UPC academic community 
Combinatòria : Problemes
Noy Serrano, Marcos; Serra Albó, Oriol (Universitat Politècnica de Catalunya, 1997)
Lecture notes
Open Access 
Combinatòria : Problemes
Serra Albó, Oriol; Noy Serrano, Marcos (Universitat Politècnica de Catalunya, 1997)
Lecture notes
Open Access 
Counting outerplanar maps
Geffner, I.; Noy Serrano, Marcos (20170413)
Article
Open AccessA 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
Noy Serrano, Marcos; Rué Perna, Juan José (200810)
Article
Open AccessFor 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
Noy Serrano, Marcos; Rasendrahasina, Vonjy; Ravelomanana, Vlady; Rué Perna, Juan José (Elsevier, 20210401)
Article
Open AccessLet 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
Noy Serrano, Marcos; Rué Perna, Juan José (Universidad de Valladolid, 2006)
Conference lecture
Restricted access  publisher's policyEn este trabajo obtenemos expresiones explícitas de las funciones generadoras de las triangulaciones y cuadrangulaciones del espacio topológico correspondiente a la supresión de un nágono del plano proyectivo real. En el ... 
Enumeration of labeled 4regular planar graphs
Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (20170801)
Article
Open AccessIn this extended abstract, we present the first combinatorial scheme for counting labeled 4regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function ... 
Enumeration of labelled 4regular planar graphs
Noy Serrano, Marcos; Requilé, Clément; Rué Perna, Juan José (20190801)
Article
Open AccessWe present the first combinatorial scheme for counting labelled 4regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function of labelled 4regular ... 
Further results on random cubic planar graphs
Noy Serrano, Marcos; Requilé, Clément; Rué Perna, Juan José (202006)
Article
Open AccessWe 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
Hernando Martín, María del Carmen; Hurtado Díaz, Fernando Alfredo; Márquez Pérez, Alberto; Mora Giné, Mercè; Noy Serrano, Marcos (1997)
Article
Open AccessGiven a set $P$ of points in the plane, the geometric tree graph of $P$ is defined as the graph $T(P)$ whose vertices are noncrossing rectilinear spanning trees of $P$, and where two trees $T_1$ and $T_2$ are adjacent ... 
Graph classes with given 3connected components: asymptotic counting, limit laws and critical phenomena
Giménez Llach, Omer; Noy Serrano, Marcos; Rué Perna, Juan José (Edicions de la Universitat de Lleida (UdL), 2008)
Conference lecture
Restricted access  publisher's policyConsider a family T of 3connected graphs, and let G be the class of graphs whose 3connected components are graphs in T . We present a general framework for analyzing such graphs classes based on singularity analysis of ... 
Graphs of noncrossing perfect matchings
Hernando Martín, María del Carmen; Hurtado Díaz, Fernando Alfredo; Noy Serrano, Marcos (2001)
Article
Open AccessLet 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 noncrossing graphs and multigraphs
Albiol, Rubén; Noy Serrano, Marcos (200812)
Article
Restricted access  publisher's policyWe refine an identity between the numbers of certain noncrossing 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
Noy Serrano, Marcos; Rasendrahasina, Vonjy; Ravelomanana, Vlady; Rué Perna, Juan José (Society for Industrial and Applied Mathematics (SIAM), 2017)
Conference report
Open AccessConsider the ErdosRenyi 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
Larrauri Borroto, Lázaro Alberto; Müller, Tobias; Noy Serrano, Marcos (20210818)
Article
Open AccessLet Gn be the binomial random graph G(n, p = c/n) in the sparse regime, which as is wellknown undergoes a phase transition at c = 1. Lynch (Random Structures Algorithms, 1992) showed that for every first order sentence ...