Browsing by Subject "Politops"
Now showing items 1-13 of 13
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An Introduction to Polytope Theory through Ehrhart's Theorem
(Universitat Politècnica de Catalunya, 2019-10)
Master thesis
Open AccessA 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 -
Constructing neighborly polytopes and oriented matroids
(2012)
Conference lecture
Open AccessA d-polytope P is neighborly if every subset of b d 2 c vertices is a face of P. In 1982, Shemer introduced a sewing construction that allows to add a vertex to a neighborly polytope in such a way as to obtain a new ... -
Exploiting symmetry on the Universal Polytope
(2012)
Conference report
Restricted access - publisher's policyThe 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 AccessWe 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 AccessIn 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 AccessIn 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 AccessWe 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 AccessThe 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) ≤ ... -
Positive Plücker tree certificates for non-realizability
(2024-01)
Article
Open AccessWe introduce a new method for finding a non-realizability certificate of a simplicial sphere S: we exhibit a monomial combination of classical 3-term Pl¨ucker relations that yields a sum of products of determinants that ... -
Prodsimplicial-neighborly polytopes
(2010-11)
Article
Open AccessWe 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 ... -
The rotation graph of k-ary trees is Hamiltonian
(Crete University Press, 2006)
Article
Restricted access - publisher's policyIn 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 ...
