Now showing items 1-14 of 14

• #### 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 ...
• #### An Introduction to Polytope Theory through Ehrhart's Theorem ﻿

(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 ﻿

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

(2005)
Article
Open Access
• #### 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, ...
• #### 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 ...
• #### 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) ≤ ...
• #### 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 ...
• #### Robust Fault Detection using Polytope-based Set-membership Consistency Test ﻿

(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 ﻿

(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 ...