Now showing items 1-14 of 14

    • An explicit construction for neighborly centrally symmetric polytopes 

      Pfeifle, Julián (2006-06-29)
      Article
      Open Access
      We give an explicit construction, based on Hadamard matrices, for an infinite series of $\big\lfloor\frac12\sqrt{d}\big\rfloor$-neighborly centrally symmetric $d$-dimensional polytopes with $4d$~vertices. This ...
    • An Introduction to Polytope Theory through Ehrhart's Theorem 

      Cano Córdoba, Filip (Universitat Politècnica de Catalunya, 2019-10)
      Master thesis
      Open Access
      A classic introduction to polytope theory is presented, serving as the foundation to develop more advanced theoretical tools, namely the algebra of polyhedra and the use of valuations. The main theoretical objective is the ...
    • Basis expansions and roots of Ehrhart polynomials 

      Pfeifle, Julián; Beck, Matthias; Loera, Jesús de; Develin, Mike; Richard, Stanley (2004)
      Article
      Open Access
    • Bounding the volume of facet-empty lattice tetrahedra 

      Pfeifle, Julián; Duong, Han; Haase, Christian; Reznick, Bruce (2005)
      Article
      Open Access
    • Dissections, Hom-complexes and the Cayley trick 

      Pfeifle, Julián (2006-06-27)
      Article
      Open Access
      We show that certain canonical realizations of the complexes $\Hom(G,H)$ and $\Hom_+(G,H)$ of (partial) graph homomorphisms studied by Babson and Kozlov are in fact instances of the polyhedral Cayley trick. For $G$~a ...
    • Exploiting symmetry on the Universal Polytope 

      Pfeifle, Julián (2012)
      Conference report
      Restricted access - publisher's policy
      The most successful method to date for finding lower bounds on the number of simplices needed to triangulate a given polytope P involves optimizing a linear functional over the associated Universal Polytope U(P). However, ...
    • Graph operations and Laplacian eigenpolytopes 

      Padrol Sureda, Arnau; Pfeifle, Julián (2010-07)
      Conference report
      Open Access
      We introduce the Laplacian eigenpolytopes ("L-polytopes") associated to a simple undirected graph G, investigate how they change under basic operations such as taking the union, join, complement, line graph and cartesian ...
    • Kalai's squeezed 3-spheres are polytopal 

      Pfeifle, Julián (2002)
      Article
      Open Access
      In 1988, Kalai [5] extended a construction of Billera and Lee to produce many triangulated(d−1)-spheres. In fact, in view of upper bounds on the number of simplicial d-polytopes by Goodman and Pollack [2, 3], he derived ...
    • Kalai's squeezed three-spheres are polytopal 

      Pfeifle, Julián (2001)
      Article
      Open Access
      In 1988, Kalai [5] extended a construction of Billera and Lee to produce many triangulated(d−1)-spheres. In fact, in view of upper bounds on the number of simplicial d-polytopes by Goodman and Pollack [2,3], he derived ...
    • On polytopality of Cartesian products of graphs 

      Pfeifle, Julián; Pilaud, Vincent; Santos Pérez, Francisco Javier (2010-07)
      Conference report
      Open Access
      We study the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we prove that a product of graphs is the graph of a simple polytope if and only if its factors are. On the other hand, we provide ...
    • On the monotone upper bound problem 

      Pfeifle, Julián; Ziegler, Günter M. (2004)
      Article
      Open Access
      The Monotone Upper Bound Problem asks for the maximal number M(d,n) of vertices on a strictly-increasing edge-path on a simple d-polytope with n facets. More specifically, it asks whether the upper bound M(d,n) ≤ ...
    • Prodsimplicial-neighborly polytopes 

      Matschke, Benjamin; Pfeifle, Julián; Pilaud, Vincent (2010-11)
      Article
      Open Access
      We introduce PSN polytopes whose k-skeleton is combinatorially equivalent to that of a product of r simplices. They simultaneously generalize both neighborly and neighborly cubical polytopes. We construct PSN polytopes ...
    • Robust Fault Detection using Polytope-based Set-membership Consistency Test 

      Blesa Izquierdo, Joaquim; Puig Cayuela, Vicenç; Saludes Closa, Jordi (2010)
      Conference report
      Open Access
      This article proposes a robust set-membership fault detection method based on the use of polytopes to bound the parameter uncertainty set. The proposed polytope-based fault detection algorithm is able to handle systems ...
    • The rotation graph of k-ary trees is Hamiltonian 

      Huemer, Clemens; Hurtado Díaz, Fernando Alfredo; Pfeifle, Julián (Crete University Press, 2006)
      Article
      Restricted access - publisher's policy
      In this paper we show that the graph of k-ary trees, connected by rotations, contains a Hamilton cycle. Our proof is constructive and thus provides a cyclic Gray code for k-ary trees. Furthermore, we identify a basic ...