Related papers: Gerechte Designs with Rectangular Regions
The aim of this article is to give a rigorous geometric interpretation of the completion of a ring with respect to an ideal. To this end, we define the infinitesimal neighbourhood of an immersion of formal schemes as the largest possible…
The real numbers are important in both mathematics and computation theory. Computationally, real numbers can be represented in several ways; most commonly using inexact floating-point data-types, but also using exact arbitrary-precision…
Locally recoverable codes (LRCs) have emerged as fundamental objects in modern coding theory, primarily due to their pivotal role in distributed and cloud storage systems. A major breakthrough in their construction was achieved by Tamo and…
Interaction between clique number $\omega(G) $ and chromatic number $\chi(G) $ of a graph is a well studied topic in graph theory. Perfect Graph Theorems are probably the most important results in this direction. Graph $G$ is called…
This paper presents a somewhat exhaustive study on the conformable fractional Gauss hypergeometric function (CFGHF). We start by solving the conformable fractional Gauss hypergeometric equation (CFGHE) about the fractional regular singular…
We develop \emph{Fra\"iss\'e theory}, namely the theory of \emph{Fra\"iss\'e classes} and \emph{Fra\"iss\'e limits}, in the context of metric structures. We show that a class of finitely generated structures is Fra\"iss\'e if and only if it…
We study geometric representations of GL(n,R) for a ring R. The structure of the associated Hecke algebras is analyzed and shown to be cellular. Multiplicities of the irreducible constituents of these representations are linked to the…
We show that a rectangle triangle random tiling with a tenfold symmetric phase is solvable by Bethe Ansatz. After the twelvefold square triangle and the eightfold rectangle triangle random tiling, this is the third example of a rectangle…
A selfsimiar manifold is a Riemannian manifold $\left(M,g\right)$ endowed with a homothetic vector field $\xi$. We characterize global selfsimilar manifolds and describe the structure of local selfsimilar manifolds. We prove that any…
We show that totally real elliptic Lefschetz fibrations that admit a real section are classified by their "real loci" which is nothing but an $S^1$-valued Morse function on the real part of the total space. We assign to each such real locus…
Classic cake-cutting algorithms enable people with different preferences to divide among them a heterogeneous resource (``cake''), such that the resulting division is fair according to each agent's individual preferences. However, these…
We approach a problem of realising algebraic objects in a certain universal equivariant stable homotopy theory; the global homotopy theory of Schwede. Specifically, for a global ring spectrum $R$, we consider which classes of ring…
A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure has a…
The representation ring of an affine algebraic group scheme can be endowed with the structure of a (special) $\lambda$-ring. We show that the same is true for the ring of symmetric representations, i.e. for the Grothendieck-Witt ring of the…
Given a planar straight-line graph $G=(V,E)$ in $\mathbb{R}^2$, a \emph{circumscribing polygon} of $G$ is a simple polygon $P$ whose vertex set is $V$, and every edge in $E$ is either an edge or an internal diagonal of $P$. A circumscribing…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
We address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the…
Optimal experimental design seeks to determine the most informative allocation of experiments to infer an unknown statistical quantity. In this work, we investigate the optimal design of experiments for {\em estimation of linear functionals…
A geometric graph is a graph whose vertex set is a set of points in the plane and whose edge set contains straight-line segments. A matching in a graph is a subset of edges of the graph with no shared vertices. A matching is called perfect…
We present HeLEx, a framework for determining the functional layout of heterogeneous spatially-configured elastic Coarse-Grained Reconfigurable Arrays (CGRAs). Given a collection of input data flow graphs (DFGs) and a target CGRA, the…