Now showing items 1-20 of 31

    • A solution to the tennis ball problem 

      Mier Vinué, Anna de; Noy Serrano, Marcos (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 

      Felsner, Stefan; Fusy, Éric; Noy Serrano, Marcos; Orden, David (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 

      Noy Serrano, Marcos (Universitat Politècnica de Catalunya, 2021-01-12)
      Exam
      Restricted access to the UPC academic community
    • CÀLCUL EN UNA VARIABLE 

      Noy Serrano, Marcos (Universitat Politècnica de Catalunya, 2020-10-26)
      Exam
      Restricted access to the UPC academic community
    • CÀLCUL EN UNA VARIABLE | (Examen extraordinari) 

      Noy Serrano, Marcos (Universitat Politècnica de Catalunya, 2019-07-01)
      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 (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 

      Noy Serrano, Marcos; Rué Perna, Juan José (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) ...
    • 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 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 

      Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (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 

      Noy Serrano, Marcos; Requilé, Clément; Rué Perna, Juan José (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 

      Noy Serrano, Marcos; Requilé, Clément; Rué Perna, Juan José (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 

      Hernando Martín, María del Carmen; Hurtado Díaz, Fernando Alfredo; Márquez Pérez, Alberto; Mora Giné, Mercè; Noy Serrano, Marcos (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 

      Giménez Llach, Omer; Noy Serrano, Marcos; Rué Perna, Juan José (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 

      Hernando Martín, María del Carmen; Hurtado Díaz, Fernando Alfredo; Noy Serrano, Marcos (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 

      Albiol, Rubén; Noy Serrano, Marcos (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 

      Noy Serrano, Marcos; Rasendrahasina, Vonjy; Ravelomanana, Vlady; Rué Perna, Juan José (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 ...
    • On matroids determined by their Tutte polynomials 

      Mier Vinué, Anna de; Noy Serrano, Marcos (2005)
      Article
      Restricted access - publisher's policy
      A matroid is T-unique if it is determined up to isomorphism by its Tutte polynomial. Known T-unique matroids include projective and affine geometries of rank at least four, wheels, whirls, free and binary spikes, and certain ...
    • On the diameter of random planar graphs 

      Chapuy, G.; Fusy, Éric; Giménez Llach, Omer; Noy Serrano, Marcos (2015)
      Article
      Open Access
      We show that the diameter diam(Gn) of a random labelled connected planar graph with n vertices is equal to n1/4+o(1) , in probability. More precisely, there exists a constant c > 0 such that {equation presented} for ˜ small ...