Related papers: Strongly dominant weight polytopes are cubes
The theory of elliptic pairs, as investigated in a paper by Castravet, Laface, Tevelev, and Ugaglia, provides useful conditions to determine polyhedrality of the pseudo-effective cone, which give rise to interesting arithmetic questions…
We establish a connection between the orbifold cohomology of hypertoric varieties and the Ehrhart theory of Lawrence polytopes. More specifically, we show that the dimensions of the orbifold cohomology groups of a hypertoric variety are…
We call the $\delta$-vector of an integral convex polytope of dimension $d$ flat if the $\delta$-vector is of the form $(1,0,\ldots,0,a,\ldots,a,0,\ldots,0)$, where $a \geq 1$. In this paper, we give the complete characterization of…
We consider products of two Macdonald polynomials of type A, indexed by dominant weights which are respectively a multiple of the first fundamental weight and a weight having zero component on the k-th fundamental weight. We give the…
Rooted, weighted continuum random trees are used to describe limits of sequences of random discrete trees. Formally, they are random quadruples $(\mathcal{T},d,r,p)$, where $(\mathcal{T},d)$ is a tree-like metric space, $r\in\mathcal{T}$ is…
We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set,…
We consider a novel version of the classical Jacquet-Langlands {correspondence}, explore a $p$-adic extension of the Jacquet-Langlands correspondence, and as an explicit example we find an overconvergent automorphic form of weight~1 which…
A codeword is associated to a linearized polynomial. The weight distribution of the codewords is determined as the linearized polynomial varies in a family of fixed degree. There is a corresponding result on Wenger graphs from linearized…
We obtain the strong asymptotics of polynomials $p_n(\lambda)$, $\lambda\in\mathbb{C}$, orthogonal with respect to measures in the complex plane of the form $$ e^{-N(|\lambda|^{2s}-t\lambda^s-\overline{t\lambda}^s)}dA(\lambda), $$ where $s$…
We examine dimensional types of scattered $P$-spaces of weight $\omega_1$. Such spaces can be embedded into $\omega_2$. There are established similarities between dimensional types of scattered separable metric spaces and dimensional types…
We use the differential algebra of polytopes to explain the known remarkable relation of the combinatorics of the associahedra and permutohedra with the universal compositional and multiplicative inversion formulas for the formal power…
We give a combinatorial formula for the Ehrhart coefficients of a certain class of weighted multi-hypersimplices. In a special case, where these polytopes coincide with the base polytope of the panhandle matroid $\textrm{Pan}_{k,n-2,n}$, we…
Let $\Delta$ be a Delzant polytope in ${\mathbb R}^n$ and ${\bf b}\in{\mathbb Z}^n$. Let $E$ denote the symplectic fibration over $S^2$ determined by the pair $(\Delta, {\bf b})$. We prove the equivalence between the fact that $(\Delta,…
Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G,\lambda)=\sum_{i=0}^{n} d(G,i) \lambda^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$. Every root of $D(G,\lambda)$ is…
In this paper, we generalize a result by Berman and Billig on weight modules over Lie algebras with polynomial multiplication. More precisely, we show that a highest weight module with an exp-polynomial ``highest weight'' has finite…
Spherically symmetric equilibrium configurations of perfect fluid obeying a polytropic equation of state are studied in spacetimes with a repulsive cosmological constant. The configurations are specified in terms of three parameters---the…
We introduce a quantitative version of polynomial cohomology for discrete groups and show that it coincides with usual group cohomology when combinatorial filling functions are polynomially bounded. As an application, we show that Betti…
A real algebraic variety is maximal (with respect to the Smith-Thom inequality) if the sum of the Betti numbers (with $\mathbb{Z}_2$ coefficients) of the real part of the variety is equal to the sum of Betti numbers of its complex part. We…
We show that certain weighted Fibonacci and Lucas series can always be expressed as linear combinations of polylogarithms. In some special cases we evaluate the series in terms of Bernoulli polynomials, making use of the connection between…
We give a cohomological and geometrical interpretation for the weighted Ehrhart theory of a full-dimensional lattice polytope $P$, with Laurent polynomial weights of geometric origin. For this purpose, we calculate the motivic Chern and…