Related papers: Unicity Concepts for Sudoku
The solution set of a system of polynomial equations typically contains ill-behaved, singular points. Resolution is a fundamental process in geometry in which we replace singular points with smooth points, while keeping the rest of the…
Hironaka's concept of characteristic polyhedron of a singularity has been one of the most powerful and fruitful ideas of the last decades in singularity theory. In fact, since then combinatorics have become a major tool in many important…
A symmetry group for Sudoku is complete if its action partitions the set of Sudoku boards into all possible orbits, and minimal if no group of smaller size would do the same. Previously, for a 4 x 4 Sudoku variation known as Shidoku, the…
We introduce a 3-dimensional categorical structure which we call intercategory. This is a kind of weak triple category with three kinds of arrows, three kinds of 2-dimensional cells and one kind of 3-dimensional cells. In one dimension, the…
We consider the problem of deciding if a set of quantum one-qudit gates $\mathcal{S}=\{U_1,\ldots,U_n\}$ is universal. We provide the compact form criteria leading to a simple algorithm that allows deciding universality of any given set of…
The restriction and Kakeya problems in Euclidean space have received much attention in the last few decades, and are related to many problems in harmonic analysis, PDE, and number theory. In this paper we initiate the study of these…
We describe the generic singularity of a Schubert variety of type A on each irreducible component of its singular locus. This singularity is given either by a cone of rank one matrices, or a quadratic cone.
We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…
Contexts are terms with one `hole', i.e. a place in which we can substitute an argument. In context unification we are given an equation over terms with variables representing contexts and ask about the satisfiability of this equation.…
The paper considers implementations of some randomized algorithms in connection with obtaining a random $n^2 \times n^2$ Sudoku matrix with programming language C++. For this purpose we describes the set $\Pi_n$ of all $(2n) \times n$…
We introduce the notion of Differential Sequences of ordinary differential equations. This is motivated by related studies based on evolution partial differential equations. We discuss the Riccati Sequence in terms of symmetry analysis,…
An algorithm for resolution of singularities in characteristic zero is described. It is expressed in terms of multi-ideals, that essentially are defined as a finite sequence of pairs, each one consiting of a sheaf of ideals and a positive…
A unified matrix-vector representation is developed of such solution concepts as the core, the uncovered, the uncaptured, the minimal weakly stable, the minimal undominated, the minimal dominant and the untrapped sets. We also propose…
Let $n=hw$, where $h$ and $w$ are integers with $h,w \ge 2$. We determine the set of possible intersection numbers of two $n \times n$ latin squares having the additional `Sudoku' constraint based on a $w \times h$ grid of $h \times w$…
We begin by considering the expectations of the creators of VisiCalc, the first spreadsheet. The emphasis is on the nature of the spreadsheet grid. The grid is taken as a presentational method for showing a solution to a Sudoku puzzle. We…
We study uniqueness of solutions to degenerate parabolic problems, posed in bounded domains, where no boundary conditions are imposed. Under suitable assumptions on the operator, uniqueness is obtained for solutions that satisfy an…
Optical singularities, which are positions within an electromagnetic field where certain field parameters become undefined, hold significant potential for applications in areas such as super-resolution microscopy, sensing, and…
We consider a sequence of sums of powers of the the roots of the cubic equation characterizing the Tribonacci sequences and derive its relationship with a particular Tribonacci sequence. Then we make a conjecture on the possible…
In this paper, we introduce a set of tools for providing user-friendly explanations in an explanation-based constraint programming system. The idea is to represent the constraints of a problem as an hierarchy (a tree). Users are then…
We begin by introducing an extension of the traditional abundancy index to imaginary quadratic rings with unique factorization. After showing that many of the properties of the traditional abundancy index continue to hold in our extended…