Related papers: A State Polytope Decomposition Formula
The paper studies constructions of irreducible polynomials over finite fields using polynomial composition method.
An algorithm for computing power conjugate presentations for finite soluble quotients of predetermined structure of finitely presented groups is described. Practical aspects of an implementation are discussed.
We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…
The normalization of scattering states is more than a rote step necessary to calculate expectation values. This normalization actually contains important information regarding the density of the scattering spectrum (along with useful…
We present a family of 3--qubit states to which any arbitrary state can be depolarized. We fully classify those states with respect to their separability and distillability properties. This provides a sufficient condition for…
We generalize the logarithmic decomposition theorem of Deligne-Illusie to a filtered version. There are two applications. The easier one provides a mod $p$ proof for a vanishing theorem in characteristic zero. The deeper one gives rise to a…
We apply combinatorial methods to a geometric problem: the classification of polytopes, in terms of Minkowski decomposability. Various properties of skeletons of polytopes are exhibited, each sufficient to guarantee indecomposability of a…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
A planar set $P$ is said to be cover-decomposable if there is a constant $k=k(P)$ such that every $k$-fold covering of the plane with translates of $P$ can be decomposed into two coverings. It is known that open convex polygons are…
We provide a necessary and sufficient condition for separability of Gaussian states of bipartite systems of arbitrarily many modes. The condition provides an operational criterion since it can be checked by simple computation. Moreover, it…
In this article we will derive a combinatorial formula for the partition function p(n). In the second part of the paper we will establish connection between partitions and q-binomial coefficients and give new interpretation for q-binomial…
A versatile new approach for calculating the depletion potential in a hard sphere mixture is presented. This is valid for any number of components and for arbitrary densities. We describe two different routes to the depletion potential for…
Let $A$ be a finite-dimensional algebra over an algebraically closed field $\Bbbk$. For any finite-dimensional $A$-module $M$ we give a general formula that computes the indecomposable decomposition of $M$ without decomposing it, for which…
We present a polynomial time algorithm to compute any fixed number of the highest coefficients of the Ehrhart quasi-polynomial of a rational simplex. Previously such algorithms were known for integer simplices and for rational polytopes of…
By means of a partial wave decomposition, we separate their contributions to the equation of state of symmetric nuclear matter for the N3LO pseudo-potential. In particular, we show that although both the tensor and the spin-orbit terms do…
For given depth of a we derive a formula for the depth of the image of that term under a given hypersubstitution.
We give a formula for the coefficients of the Yablonskii-Vorob'ev polynomial. Also the reduction modulo a prime number of the polynomial is studied.
We classify here combinatorially rigid simple polytopes with three facets more than their dimension.
Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…
We give an invariant formula for a star product with separation of variables on a pseudo-Kahler manifold.