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 ...

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 ...

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 ...

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 ...

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 ...

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) ≤ ...