MD - Matemàtica Discreta

 

Investigació en els camps de combinatòria enumerativa, combinatòria algebraica i teoria de grafs.

http://futur.upc.edu/MD

The aim is to carry out research in the fields of enumerative combinatorics, algebraic combinatorics and graph theory.

http://futur.upc.edu/MD

The aim is to carry out research in the fields of enumerative combinatorics, algebraic combinatorics and graph theory.

http://futur.upc.edu/MD

Recent Submissions

  • On the number of labeled graphs of bounded treewidth 

    Baste, Julien; Noy Serrano, Marcos; Sau, Ignasi (2018-06-01)
    Article
    Open Access
    Let be Tnk the number of labeled graphs on vertices and treewidth at most (equivalently, the number o<f labeled partial -trees). We show that [...] for k>1 and some explicit absolute constant c>0. Disregarding terms depending ...

  • El arte de contar: combinatoria y enumeración 

    Rué Perna, Juan José (RBA Libros, 2011-06-01)
    Book
    Restricted access - publisher's policy
    Muchas de las preguntas más importantes de las matemáticas modernas requieren dominar un arte muy especial: el de contar. La rama de las matemáticas que ha hecho del enumerar un arte se llama combinatoria, y de la mano de ...

  • Los números trascendentes 

    Fresán, Javier; Rué Perna, Juan José (Ediciones La Catarata, 2013-05)
    Book
    Restricted access - publisher's policy
    La expresión e¿ v163 es mucho más que la suma de sus partes e, ¿ y v163. Lejos de ser una elección casual, esta fórmula sirve a los autores de hilo conductor para adentrase en las áreas de la investigación más activa de ...

  • Transformation and decomposition of clutters into matroids 

    Martí Farré, Jaume; Mier Vinué, Anna de (2017-05-25)
    Article
    Open Access
    A clutter is a family of mutually incomparable sets. The set of circuits of a matroid, its set of bases, and its set of hyperplanes are examples of clutters arising from matroids. In this paper we address the question of ...

  • On trees with the same restricted U-polynomial and the Prouhet–Tarry–Escott problem 

    Aliste Prieto, José; Mier Vinué, Anna de; Zamora, José (2017-06)
    Article
    Open Access
    This paper focuses on the well-known problem due to Stanley of whether two non-isomorphic trees can have the same U-polynomial (or, equivalently, the same chromatic symmetric function). We consider the Uk-polynomial, which ...

  • Threshold functions and Poisson convergence for systems of equations in random sets 

    Rué Perna, Juan José; Spiegel, Christoph; Zumalacárregui, Ana (2017-05-10)
    Article
    Open Access
    We study threshold functions for the existence of solutions to linear systems of equations in random sets and present a unified framework which includes arithmetic progressions, sum-free sets, Bh[g]Bh[g]-sets and Hilbert ...

  • Corrigendum to"On the limiting distribution of the metric dimension for random forests" [European J. Combin. 49 (2015) 68-89] 

    Mitsche, Dieter; Rué Perna, Juan José (2017-07-22)
    Article
    Open Access
    In the paper ”On the limiting distribution of the metric dimension for random forests” the metric dimension ß(G) of sparse G(n, p) with p = c/n and c < 1 was studied (Theorem 1.2). In the proof of this theorem, for the ...

  • Counting configuration-free sets in groups 

    Rué Perna, Juan José; Serra Albó, Oriol; Vena Cros, Lluís (2017-01-01)
    Article
    Open Access
    © 2017 Elsevier Ltd. We provide asymptotic counting for the number of subsets of given size which are free of certain configurations in finite groups. Applications include sets without solutions to equations in non-abelian ...

  • 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 ...

  • Random strategies are nearly optimal for generalized van der Waerden Games 

    Kusch, C.; Rué Perna, Juan José; Spiegel, Christoph; Szabó, T. (2017-08-01)
    Article
    Open Access
    In a (1 : q) Maker-Breaker game, one of the central questions is to find (or at least estimate) the maximal value of q that allows Maker to win the game. Based on the ideas of Bednarska and Luczak [Bednarska, M., and T. ...

  • 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 ...

  • 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 ...

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