• An involution on bicubic maps and beta(0,1)-trees 

    Claesson, Anders; Kitaev, Sergey; Mier Vinué, Anna de (2015)
    Artículo
    Acceso abierto
    Bicubic maps are in bijection with (0 ; 1)-trees. We introduce two new ways of decomposing (0 ; 1)-trees. Using this we de ne an endofunc- tion on (0 ; 1)-trees, and thus also on bicubic maps. We show that ...
  • A solution to the tennis ball problem 

    Mier Vinué, Anna de; Noy Serrano, Marcos (2005)
    Artículo
    Acceso abierto
    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 ...
  • Completion and decomposition of a clutter into representable matroids 

    Martí Farré, Jaume; Mier Vinué, Anna de (Elsevier, 2015-05-01)
    Artículo
    Acceso abierto
    This paper deals with the question of completing a monotone increasing family of subsets Gamma of a finite set Omega to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we prove ...
  • Extensions and presentations of transversal matroids 

    Bonin, Joseph; Mier Vinué, Anna de (2015-11-02)
    Artículo
    Acceso abierto
    A transversal matroid MM can be represented by a collection of sets, called a presentation of MM, whose partial transversals are the independent sets of MM. Minimal presentations are those for which removing any element ...
  • Lattice path matroids: structural properties 

    Bonin, Joseph; Mier Vinué, Anna de (2006)
    Artículo
    Acceso abierto
    This paper studies structural aspects of lattice path matroids. Among the basic topics treated are direct sums, duals, minors, circuits, and connected flats. One of the main results is a characterization of lattice path ...
  • Lower bounds on the maximum number of non-crossing acyclic graphs 

    Huemer, Clemens; Mier Vinué, Anna de (2015-08-01)
    Artículo
    Acceso abierto
    This paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of non-crossing spanning trees and forests. We show that the so-called double chain ...
  • On graphs with the same restricted U-polynomial and the U-polynomial for rooted graphs 

    Aliste Prieto, José; Zamora, José; Mier Vinué, Anna de (2018-07)
    Artículo
    Acceso restringido por política de la editorial
    In this abstract, we construct explicitly, for every k, pairs of non-isomorphic trees with the same restricted U-polynomial; by this we mean that the polynomials agree on terms with degree at most k. The construction is ...
  • On matroids determined by their Tutte polynomials 

    Mier Vinué, Anna de; Noy Serrano, Marcos (2005)
    Artículo
    Acceso restringido por política de la editorial
    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 evaluation of the Tutte polynomial at the points (1,-1) and (2,-1) 

    Goodall, Andrew; Merino, Criel; Mier Vinué, Anna de; Noy Serrano, Marcos (2010)
    Texto en actas de congreso
    Acceso abierto
    C. Merino proved recently the following identity between evaluations of the Tutte polynomial of complete graphs: t($K_{n+2}$; 1,−1) = t($K_n$;2,−1). In this work we extend this result by giving a large class of graphs with ...
  • On the maximum number of cycles in outerplanar and series-parallel graph 

    Mier Vinué, Anna de; Noy Serrano, Marcos (2009)
    Artículo
    Acceso restringido por política de la editorial
    Let c(n) be the maximum number of cycles in an outerplanar graph with n vertices. We show that lim $c(n)^{1/n}$ exists and equals β = 1.502837 . . ., where β is a constant related to the recurrence $x_n+1$=1+$x^2_n$, ...
  • 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)
    Artículo
    Acceso restringido por política de la editorial
    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 ...
  • The Tutte polynomial characterizes simple outerplanar graphs 

    Goodall, Andrew; Mier Vinué, Anna de; Noble, S.; Noy Serrano, Marcos (2011-07)
    Artículo
    Acceso restringido por acuerdo de confidencialidad
    We show that if G is a simple outerplanar graph and H is a graph with the same Tutte polynomial as G, then H is also outerplanar. Examples show that the condition of G being simple cannot be omitted.
  • Transformation and decomposition of clutters into matroids 

    Martí Farré, Jaume; Mier Vinué, Anna de (2017-05-25)
    Artículo
    Acceso restringido por política de la editorial
    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 ...
  • T-uniqueness of some families of k-chordal matroids 

    Bonin, Joseph; Mier Vinué, Anna de (2004)
    Artículo
    Acceso abierto
    We define k-chordal matroids as a generalization of chordal matroids, and develop tools for proving that some k-chordal matroids are T-unique, that is, determined up to isomorphism by their Tutte polynomials. We apply this ...
  • Tutte polynomials of generalized parallel connections 

    Bonin, Joseph; Mier Vinué, Anna de (2004)
    Artículo
    Acceso abierto
    We use weighted characteristic polynomials to compute Tutte polynomials of generalized parallel connections in the case in which the simplification of the maximal common restriction of the two constituent matroids is a ...