Related papers: IDP for 2-Partition Maximal Symmetric Polytopes
In this paper, we consider the problem of partitioning a polygon into a set of connected disjoint sub-polygons, each of which covers an area of a specific size. The work is motivated by terrain covering applications in robotics, where the…
We give an explicit construction, based on Hadamard matrices, for an infinite series of floor{sqrt{d}/2}-neighborly centrally symmetric d-dimensional polytopes with 4d vertices. This appears to be the best explicit version yet of a recent…
Given an odd prime $p$, we identify composition factors of the reduction modulo $p$ of spin irreducible representations of the covering groups of symmetric groups indexed by partitions with 2 parts and find some decomposition numbers.
We study the equipotential surfaces around of a two particle system in 3-d under a pairwise good potential as the one of Van der Waals. The level sets are completely determined by the solutions of polynomials of at most fourth degree that…
We consider a class of $0$-$1$ polynomial programming termed multiple choice polynomial programming (MCPP) where the constraint requires exact one component per subset of the partition to be $1$ after all the entries are partitioned.…
The extension complexity of a polytope measures its amenability to succinct representations via lifts. There are several versions of extension complexity, including linear, real semidefinite, and complex semidefinite. We focus on the last…
A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike…
We provide simple criteria and algorithms for expressing homogeneous polynomials as sums of powers of independent linear forms, or equivalently, for decomposing symmetric tensors into sums of rank-1 symmetric tensors of linearly independent…
We study a class of overdetermined algebraic systems of equations. We prove that the number of distinct solutions equals to the maximal possible if and only if certain matrices are commuting and semisimple. This gives a characterization of…
We show that one can enumerate the vertices of the convex hull of integer points in polytopes whose constraint matrices have bounded and nonzero subdeterminants, in time polynomial in the dimension and encoding size of the polytope. This…
The assignments of a set of $m$ items into $n$ clusters of prescribed sizes $k_1,\dots,k_n$ can be encoded as the vertices of the partition polytope $\mathrm{PP}(k_1,\dots,k_n)$. We prove that, if $K = \max\{k_1,\dots,k_n\}$, then the…
We develop a collection of numerical algorithms which connect ideas from polyhedral geometry and algebraic geometry. The first algorithm we develop functions as a numerical oracle for the Newton polytope of a hypersurface and is based on…
We determine the extreme points and facets of the convex hull of all dual degree partitions of simple graphs on $n$ vertices.
We build free, bigraded bidifferential algebra models for the forms on a complex manifold, with respect to a strong notion of quasi-isomorphism and compatible with the conjugation symmetry. This answers a question of Sullivan. The resulting…
The partial breaking of supersymmetry in flat space can be accomplished using any one of three dual representations for the massive N=1 spin-3/2 multiplet. Each of the representations can be ``unHiggsed'', which gives rise to a set of dual…
The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space $\mathbb{R}^3$ are easier to feel by human's intuition. We give the maximum order of finite group actions on $(\mathbb{R}^3, \Sigma)$…
We describe a decomposition algorithm for elliptic multiple zeta values, which amounts to the construction of an injective map $\psi$ from the algebra of elliptic multiple zeta values to a space of iterated Eisenstein integrals. We give…
By [R. Bautista, P. Gabriel, A.V Roiter., L. Salmeron, Representation-finite algebras and multiplicative basis. Invent. Math. 81 (1985) 217-285.], a finite-dimensional algebra having finitely many isoclasses of indecomposable…
In this paper, we prove an optimal isoperimetric inequality for spacelike, compact, star-shaped, and $2$-convex hypersurfaces in de Sitter space.
We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a four-fold, rational (Feynman-)parametric representation…