10 citations · 49 across the 34 of their papers we have counts for
46 papers
A 4-Dimensional Peabody of Constant Width
Isaac Arelio, Luis Montejano, Deborah Oliveros
In this paper we present a unique 4-dimensional body of constant width based on the classical notion of focal conics.
On -neighborly reorientations of oriented matroids
Rangel Hernández-Ortiz, Kolja Knauer, Luis Pedro Montejano
We study the existence and the number of -neighborly reorientations of an oriented matroid. This leads to -variants of McMullen's problem and Roudneff's conjecture, the case…
Roudneff's Conjecture in Dimension
Rangel Hernández-Ortiz, Kolja Knauer, Luis Pedro Montejano +1
J.-P. Roudneff conjectured in 1991 that every arrangement of pseudohyperplanes in the real projective space has at most $\sum_{i=0}^{d-2} \binom{n-…
An overview of complex ellipsoids
Jorge Luis Arocha, Javier Bracho, Luis Montejano
An ellipsoid is the image of a ball under an affine transformation. If this affine transformation is over the complex numbers, we refer to it as a complex ellipsoid. Characterizati…
Self-dual Maps III: projective links
L. Montejano, J. Ramirez Alfonsin, I. Rasskin
In this paper, we present necessary and sufficient combinatorial conditions for a link to be projective, that is, a link in . This characterization is closely related to the…
Reflections of convex bodies and their sections
Jorge L. Arocha, Javier Bracho, Luis Montejano
The purpose of this paper is to study the reflections of a convex body. In particular, we are interested in orthogonal reflections of its sections that can be extended to reflectio…
Complex ellipsoids and complex symmetry
Jorge Arocha, Javier Bracho, Luis Montejano
Several characterizations of complex ellipsoids among convex bodies in Cn, in terms of their sections and projections are proved. Characterizing complex symmetry in similar terms i…
A new and simple proof of the false centre theorem
Luis Montejano, Efren Morales-Amaya
We present in this work a new and simple proof of the false centre theorem.
Convex bodies all whose sections (projections) are equal
Luis Montejano
The purpose of this paper is to answer the following question: If all hyperplane sections through the origin of a convex body are "equal", is the convex body "equal" to the ball? T…
A short proof of Kneser's theorem via transversals
Luis Montejano
A very short proof of Kneser's theorem via transversal is given.
Peabodies of Constant Width
Isaac Arelio, Luis Montejano, Deborah Oliveros
The purpose of this paper is to describe a new -dimensional family of bodies of constant width that we have called peabodies, obtained from the Reuleaux tetrahedron by replacing…
Self-dual maps II: links and symmetry
Luis Montejano, Jorge L. Ramírez Alfonsín, Ivan Rasskin
In this paper, we investigate representations of links that are either centrally symmetric in or antipodally symmetric in . By using the notions of ant…
Extremal inscribed and circumscribed complex ellipsoids
Jorge L. Arocha, Javier Bracho, Luis Montejano
We prove that if a convex set in Cn contains two inscribed complex ellipsoid of maximal volume then one is a translate of the other. On the other hand, the circumscribed complex el…
Self-dual Maps I : antipodality
Luis Montejano, Jorge L. Ramírez Alfonsín, Ivan Rasskin
A self-dual map is said to be \emph{antipodally self-dual} if the dual map is antipodal embedded in with respect to . In this paper, we investigate nece…
Italian domination in rooted product graphs
R. Hernandez-Ortiz, L. P. Montejano, J. A. Rodriguez-Velazquez
In this article, we obtain closed formulae for the Italian domination number of rooted product graphs. As a particular case of the study, we derive the corresponding formulas for c…
On the complex Banach conjecture
Javier Bracho, Luis Montejano
The complex conjecture of Stefan Banach states that if V is a Banach space over the complex numbers where for some n, 1<n<dim(V), all of its n-dimensional subspaces are isometric,…
Strongly involutive self-dual polyhedra
Javier Bracho, Luis Montejano, Eric Pauli +1
A polyhedron is a graph which is simple, planar and 3-connected. In this note, we classify the family of strongly involutive self-dual polyhedra. The latter is done by using a…
Convex Bodies with affinely equivalent projections and affine bodies of revolution
Luis Montejano
Abstract In this paper, we study affine bodies of revolution. This will allow us to prove that a convex body all whose orthogonal -projections are affinely equivalent is an elli…
The graphs behind Reuleaux polyhedra
Luis Montejano, Eric Pauli, Miguel Raggi +1
This work is about graphs arising from Reuleaux polyhedra. Such graphs must necessarily be planar, -connected and strongly self-dual. We study the question of when these conditi…
On the number of vertices of projective polytopes
Natalia García-Colín, Luis Pedro Montejano, Jorge Luis Ramírez Alfonsín
Let be a configuration of points in . What is the maximum number of vertices that can have among all the possible permissible projective transfor…
Rainbow simplices in triangulations of manifolds
Luis Montejano
Given a coloration of the vertices of a triangulation of a manifold, we give homological conditions on the chromatic complexes under which it is possible to obtain a rainbow simple…
Different versions of the nerve theorem and rainbow simplices
Frédéric Meunier, Luis Montejano
Given a simplicial complex and a collection of subcomplexes covering it, the nerve theorem, a fundamental tool in topological combinatorics, guarantees a certain connectivity of th…
Chomp on generalized Kneser graphs and others
Ignacio García-Marco, Kolja Knauer, Luis Pedro Montejano
In chomp on graphs, two players alternatingly pick an edge or a vertex from a graph. The player that cannot move any more loses. The questions one wants to answer for a given graph…
-vectors of chordal graphs
Luis Pedro Montejano, Luis Núñez Betancourt
The -vector of a graph is defined in terms of its clique vector by the equation $\sum^d_{i=1}b_i(x+1)^{i-1}=\sum^d_{i=1} c_i x^{i…