Now showing items 1-20 of 22

• #### An explicit construction for neighborly centrally symmetric polytopes ﻿

(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 ...
• #### Basis expansions and roots of Ehrhart polynomials ﻿

(2004)
Article
Open Access
• #### Bounding the volume of facet-empty lattice tetrahedra ﻿

(2005)
Article
Open Access
• #### Búsqueda de comunidades en grafos grandes mediante configuraciones implícitas de vectores ﻿

Conference report
Open Access
Presentamos el algoritmo OCA para buscar comunidades solapadas en grafos grandes, como por ejemplo la Wikipedia con 1,6×107 nodos y 1,8×108 aristas. OCA se basa en la búsqueda iterativa de subconjuntos localmente óptimos ...
• #### CÀLCUL (Examen 1r quadrimestre, 1r parcial) ﻿

(Universitat Politècnica de Catalunya, 2017-11-03)
Exam
• #### Complejos de homomorfismos y disecciones de polígonos ﻿

Conference lecture
Open Access
Encontramos realizaciones canónicas de los complejos politopales Hom(G,H)formados por homomorfismos de grafos y estudiados por Babson y Kozlov. Si G es un grafo completo, caracterizamos en qué casos cierta proyección ...
• #### Continuous symmetry and shape measures ﻿

(Centre de Recerca Matemàtica, 2010-06)
Part of book or chapter of book
Open Access
• #### DISCRETE AND ALGORITHMIC GEOMETRY | FINAL ﻿

(Universitat Politècnica de Catalunya, 2019-01-10)
Exam
• #### Dissections, Hom-complexes and the Cayley trick ﻿

(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 ﻿

(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, ...
• #### Gale duality bounds on the location of roots of polynomials with nonnegative coefficients ﻿

(2010-04)
Article
Open Access
We bound the location of roots of polynomials that have nonnegative coefficients with respect to a fixed but arbitrary basis of the vector space of polynomials of degree at most d. For this, we interpret the basis polynomials ...
• #### Graph operations and Laplacian eigenpolytopes ﻿

(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 ﻿

(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 ﻿

(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 ...
• #### MÈTODES MATEMÀTICS III (Examen 1r quadrimestre, 2n parcial) ﻿

(Universitat Politècnica de Catalunya, 2016-01-11)
Exam
• #### On polytopality of Cartesian products of graphs ﻿

(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 ﻿

(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) ≤ ...
• #### Overlapping community search for social networks ﻿

(IEEE Press. Institute of Electrical and Electronics Engineers, 2010)
Conference report
Open Access
Finding decompositions of a graph into a family of clusters is crucial to understanding its underlying structure. While most existing approaches focus on partitioning the nodes, real-world datasets suggest the presence ...
• #### Polygons as sections of higher-dimensional polytopes ﻿

(2015-02-09)
Article
Open Access
We show that every heptagon is a section of a 3-polytope with 6 vertices. This implies that every n-gon with n >= 7 can be obtained as a section of a (2 + [n/7])-dimensional polytope with at most [6n/7] vertices; and ...
• #### Prodsimplicial-neighborly polytopes ﻿

(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 ...