Related papers: Some Applications of $S$-restricted Set Partitions
In this paper we study various approaches for exploiting symmetries in polynomial optimization problems within the framework of semi definite programming relaxations. Our special focus is on constrained problems especially when the…
A Lattice is a partially ordered set where both least upper bound and greatest lower bound of any pair of elements are unique and exist within the set. K\"{o}tter and Kschischang proved that codes in the linear lattice can be used for error…
In this work, a graph partitioning problem in a fixed number of connected components is considered. Given an undirected graph with costs on the edges, the problem consists of partitioning the set of nodes into a fixed number of subsets with…
We briefly introduce several problems: (1) a generalization of the convex fair partition conjecture, (2) on non-trivial invariants among polyhedrons that can be formed from the same set of face polygons, (3) two questions on assembling…
In [2] a new factorization for infinite Hessenberg banded matrices was introduced. In this note we prove that this kind of factorization can also be used for finite matrices. In addition, a new method for solving banded linear systems is…
We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…
In this paper we extend the block combinatorics partition theorems of Hindman and Milliken in the setting of the recursive system of the block Schreier families (B^xi) consisting of families defined for every countable ordinal xi. Results…
Resonance counting is an intuitive and widely used tool in Random Matrix Theory and Anderson Localization. Its undoubted advantage is its simplicity: in principle, it is easily applicable to any random matrix ensemble. On the downside, the…
Folding a sequence $S$ into a multidimensional box is a method that is used to construct multidimensional codes. The well known operation of folding is generalized in a way that the sequence $S$ can be folded into various shapes. The new…
We introduce and study the lattice of generalized partitions, called weighted partitions. This lattice possesses similar properties of the lattice of partitions. By use of the pictorial representation of a weighted partition, the total…
Spectrahedra are sets defined by linear matrix inequalities. Projections of spectrahedra are called semidefinitely representable sets. Both kinds of sets are of practical use in polynomial optimization, since they occur as feasible sets in…
Barycentric coordinates provide solutions to the problem of expressing an element of a compact convex set as a convex combination of a finite number of extreme points of the set. They have been studied widely within the geometric…
Bosonic formulas for generating series of partitions with certain restrictions are obtained by solving a set of linear matrix q-difference equations. Some particular cases are related to combinatorial problems arising from solvable lattice…
Positive semidefinite matrices partitioned into a small number of Hermitian blocks have a remarkable property. Such a matrix may be written in a simple way from the sum of its diagonal blocks
In this short note we confirm the deep structural correspondence between the complexity of a countable scattered chain (= strict linear order) and its big Ramsey combinatorics: we show that a countable scattered chain has finite big Ramsey…
We provide a sparse version of the bounded degree SOS hierarchy BSOS [7] for polynomial optimization problems. It permits to treat large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies the…
We give a combinatorial description of shape theory using finite topological $T_0$-spaces (finite partially ordered sets). This description may lead to a sort of computational shape theory. Then we introduce the notion of core for inverse…
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…
We provide a development that unifies, simplifies and extends considerably a number of minimax results in the restricted parameter space literature. Various applications follow, such as that of estimating location or scale parameters under…