Related papers: Polyhedral combinatorics of bisectors
The main goal of this paper is to give explicit descriptions of two maximal cones in the Gr\"obner fan of the Pl\"ucker ideal. These cones correspond to the monomial ideals given by semistandard and PBW-semistandard Young tableaux. For the…
We consider (symmetric, non-degenerate) bilinear spaces over a finite field and investigate the properties of their $\ell$-complementary subspaces, i.e., the subspaces that intersect their dual in dimension $\ell$. This concept generalizes…
We consider the systems of diffusion-orthogonal polynomials, defined in the work [1] of D. Bakry, S. Orevkov and M. Zani and (particularly) explain why these systems with boundary of maximal possible degree should always come from the…
We present a simple algorithm for determining the extremal points in Euclidean space whose convex hull is the nth polytope in the sequence known as the multiplihedra. This answers the open question of whether the multiplihedra could be…
We demonstrate a wide-band diplexed focal plane suitable for observing low-frequency foregrounds that are important for cosmic microwave background polarimetry. The antenna elements are composed of slotted bowtie antennas with 60% bandwidth…
Huemer et al. (Discrete Math, 2019) proved that for any two finite point sets $R$ and $B$ in the plane with $|R| = |B|$, the perfect matching that matches points of $R$ with points of $B$, and maximizes the total squared Euclidean distance…
Almost four decades ago, Bergman and Milton independently showed that the isotropic effective electric permittivity of a two-phase composite material with a given volume fraction is constrained to lie within lens-shaped regions in the…
We consider the bipartite boolean quadric polytope (BQP) with multiple-choice constraints and analyse its combinatorial properties. The well-studied BQP is defined as the convex hull of all quadric incidence vectors over a bipartite graph.…
Our work explores fusions, the multidimensional counterparts of mean-preserving contractions and their extreme and exposed points. We reveal an elegant geometric/combinatorial structure for these objects. Of particular note is the…
Credal sets are one of the most important models for describing probabilistic uncertainty. They usually arise as convex sets of probabilistic models compatible with judgments provided in terms of coherent lower previsions or more specific…
We prove to all orders of renormalized perturbative polymer field theory the existence of a short chain expansion applying to polymer solutions of long and short chains. For a general polymer network with long and short chains we show…
We study the max-plus or tropical analogue of the notion of polar: the polar of a cone represents the set of linear inequalities satisfied by its elements. We establish an analogue of the bipolar theorem, which characterizes all the…
We introduce the bisector energy of an $n$-point set $P$ in $\mathbb{R}^2$, defined as the number of quadruples $(a,b,c,d)$ from $P$ such that $a$ and $b$ determine the same perpendicular bisector as $c$ and $d$. If no line or circle…
Biquadratic tensors play a central role in many areas of science. Examples include elasticity tensor and Eshelby tensor in solid mechanics, and Riemann curvature tensor in relativity theory. The singular values and spectral norm of a…
The secondary fan $\Sigma(k,n)$ is a polyhedral fan which stratifies the regular subdivisions of the hypersimplices $\Delta(k,n)$. We find new infinite families of rays of $\Sigma(k,n)$, and we compute the fans $\Sigma(2,7)$ and…
This paper is devoted to the classification problems concerning extended deformations of convex polyhedra and real hyperplane arrangements in the following senses: combinatorial equivalence of face posets, normal equivalence on normal fans…
In this paper we consider the conditions that need to be satisfied by two families of pseudofunctors with a common codomain for them to be collated into a bifunctor. We observe similarities between these conditions and distributive laws of…
Continuing our recent work we study polynomial masks of multivariate tight wavelet frames from two additional and complementary points of view: convexity and system theory. We consider such polynomial masks that are derived by means of the…
We introduce the notion of a two-scale branching function associated with an arbitrary metric space, which encodes the lower and upper box dimensions as well as the Assouad spectrum. If the metric space is quasi-doubling, this function is…
In this paper, we give a polynomial-time algorithm for deciding whether an input bipartite graph admits a 2-layer fan-planar drawing, resolving an open problem posed in several papers since 2015.