Related papers: Products of Foldable Triangulations

We consider skew-products of quadratic maps over certain Misiurewicz-Thurston maps and study their statistical properties. We prove that, when the coupling function is a polynomial of odd degree, such a system admits two positive Lyapunov…

We introduce families of two-parameter multivariate polynomials indexed by pairs of partitions $v,w$ -- biaxial double $(\beta,q)$-Grothendieck polynomials -- which specialize at $q=0$ and $v=1$ to double $\beta$-Grothendieck polynomials…

In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second--order linear partial differential equations, which are admissible potentially…

We associate root polytopes to directed graphs and study them by using ribbon structures. Most attention is paid to what we call the semi-balanced case, i.e., when each cycle has the same number of edges pointing in the two directions.…

Let $\Phi$ be an irreducible crystallographic root system and $\mathcal P$ its root polytope, i.e., its convex hull. We provide a uniform construction, for all root types, of a triangulation of the facets of $\mathcal P$. We also prove…

Brylawski's tensor product formula expresses the Tutte polynomial of the tensor product of two graphs in terms of Tutte polynomials arising from the tensor factors. We are concerned with extensions of Brylawski's tensor product formula to…

This paper generalizes the normally ordered tensor product from Tate vector spaces to Tate objects over arbitrary exact categories. We show how to lift bi-right exact monoidal structures, duality functors, and construct external Homs. We…

We introduce the notion of P-polynomial coherent configurations and show that they can have at most two fibres. We then introduce a class of two-fibre coherent configurations which have two distinguished bases for the coherent algebra,…

Cosmological polytopes of graphs are a geometric tool in physics to study wavefunctions for cosmological models whose Feynman diagram is given by the graph. After their recent introduction by Arkani-Hamed, Benincasa and Postnikov the focus…

We investigate a novel setting for polytope rigidity, where a flex must preserve edge lengths and the planarity of faces, but is allowed to change the shapes of faces. For instance, the regular cube is flexible in this notion. We present…

We study the homotopy theory of polyhedral products associated to a combinatorial generalisation of manifolds known as pseudomanifolds. As special cases, we show that loop spaces of moment-angle manifolds associated to triangulations of…

Some posets of binary leaf-labeled trees are shown to be supersolvable lattices and explicit EL-labelings are given. Their characteristic polynomials are computed, recovering their known factorization in a different way.

Symmetric product orbifolds, i.e. permutation orbifolds of the full symmetric group S_{n} are considered by applying the general techniques of permutation orbifolds. Generating functions for various quantities, e.g. the torus partition…

Polytope numbers for a polytope are a sequence of nonnegative integers that are defined by the facial information of a polytope. Every polygon is triangulable and a higher dimensional analogue of this fact states that every polytope is…

A well-known conjecture states that the Whitney numbers of the second kind of a geometric lattice (simple matroid) are logarithmically concave. We show this conjecture to be equivalent to proving an upper bound on the number of new copoints…

Building on Whitney's classical method of triangulating smooth manifolds, we show that every compact $d$-dimensional smooth manifold admits a triangulation with dual graph of twin-width at most $d^{O(d)}$. In particular, it follows that…

Given a polytope $\mathcal{P}$ in $\mathbb{R}^d$ and a subset $U$ of its vertices, is there a triangulation of $\mathcal{P}$ using $d$-simplices that all contain $U$? We answer this question by proving an equivalent and easy-to-check…

We present a procedure to generate bipartite grids for simply connected domains in 2-D and 3-D of prescribed size and controlled regularity elements. The mesh elements $K$ of the triangulation satisfy $\zeta_{K} \leq C$ where $\zeta_{K}$ is…

Orthogonal polynomials on the product domain $[a_1,b_1] \times [a_2,b_2]$ with respect to the inner product $$ \langle f,g \rangle_S = \int_{a_1}^{b_1} \int_{a_2}^{b_2} \nabla f(x,y)\cdot \nabla g(x,y)\, w_1(x)w_2(y) \,dx\, dy + \lambda…

In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved (\cite{Sa}, \cite{CaSoA}). However, the question for multidimensional Lorentz spaces is still open. In this paper,…