Related papers: Products of Foldable Triangulations
The Total Matching Polytope generalizes the Stable Set Polytope and the Matching Polytope. In this paper, we give the perfect formulation for Trees and we derive two new families of valid inequalities, the balanced biclique inequalities…
We investigate the following generalisation of the 'multiplication table problem' of Erd\H{o}s: given a bipartite graph with $m$ edges, how large is the set of sizes of its induced subgraphs? Erd\H{o}s's problem of estimating the number of…
In [{Structural properties and decomposition of linear balanced matrices}, {\it Mathematical Programming}, 55:129--168, 1992], Conforti and Rao conjectured that every balanced bipartite graph contains an edge that is not the unique chord of…
We show that the tensor product of two random linear codes is robustly testable with high probability. This implies that one can obtain pairs of linear codes such that their product and the product of their dual codes are simultaneously…
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (adjacent to an angle larger than 180 degrees. In this paper we prove that the opposite statement is also true, namely that planar…
It is well known that Pascal's triangle exhibits fractal behavior when reduced modulo a prime. We show that the triangle of Fibonomial coefficients has a similar nature modulo two. Specifically, for any $m \ge 0$, the subtriangle consisting…
We introduce constrained polynomial zonotopes, a novel non-convex set representation that is closed under linear map, Minkowski sum, Cartesian product, convex hull, intersection, union, and quadratic as well as higher-order maps. We show…
We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. In addition to divisibility and irreducibility results we also consider…
The concept of a composed product for univariate polynomials has been explored extensively by Brawley, Brown, Carlitz, Gao, Mills, et al. Starting with these fundamental ideas and utilizing fractional power series representation (in…
Kang and Park recently showed that every cubic (loopless) multigraph is incidence 6-choosable [On incidence choosability of cubic graphs. \emph{arXiv}, April 2018]. Equivalently, every bipartite graph obtained by subdividing once every edge…
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of…
The results of [1,2] on linear homogeneous two-weight codes over finite Frobenius rings are exended in two ways: It is shown that certain non-projective two-weight codes give rise to strongly regular graphs in the way described in [1,2].…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
Closed (and simply-connected) manifolds whose dimensions are larger than 4 are central geometric objects in classical algebraic topology and differential topology. They have been classified via algebraic and abstract objects. On the other…
We give a formula for the number of lozenge tilings of a hexagon on the triangular lattice with unit triangles removed from arbitrary positions along two non-adjacent, non-opposite sides. Our formula implies that for certain families of…
We show that any bijection between two root systems that preserves angles (but not necessarily lengths) gives rise to inequalities relating tensor product multiplicities for the corresponding complex semisimple Lie groups (or Lie algebras).…
We develop finite element spaces of symmetric tensor products of two-forms with polynomial coefficients. In three dimensions, these give higher order finite element spaces of matrix fields with normal-normal continuity, which have…
We compute the canonical form of the cosmological polytope for any graph in terms of the dual of the shifted cosmological polytope in two different ways. On the way, we provide an explicit coordinate description of the dual of the…
A split of a polytope $P$ is a (regular) subdivision with exactly two maximal cells. It turns out that each weight function on the vertices of $P$ admits a unique decomposition as a linear combination of weight functions corresponding to…
Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in \cite{LSX}. The main results consist of a new derivation of the Gaussian type cubature for the…