Related papers: On the Construction of Even Order Magic Squares
This article studies a generalization of magic squares to finite projective planes. In traditional magic squares the entries come from the natural numbers. This does not work for finite projective planes, so we instead use Abelian groups.…
A magic square of order $n$ with all subsquares of possible orders (ASMS$(n)$) is a magic square which contains a general magic square of each order $k\in\{3, 4, \cdots, n-2\}$. Since the conjecture on the existence of an ASMS was proposed…
Our purpose is to determine the complete set of mutually orthogonal squares of order $d$, which are not necessary Latin. In this article, we introduce the concept of supersquare of order $d$, which is defined with the help of its generating…
A \emph{magic square} is an $n \times n$ array of distinct positive integers whose sum along any row, column, or main diagonal is the same number. We compute the number of such squares for $n=4$, as a function of either the magic sum or an…
A systematic construction of higher order splines using two hierarchies of polynomials is presented. Explicit instructions on how to implement one of these hierarchies are given. The results are limited to interpolations on regular,…
This article present a new, direct and simple formula for constructing Mignotte sequences.
A construction that generates Williamson matrices of order $2n$ from Williamson matrices of odd order $n$ is presented. The construction is completely constructive and only uses three simple sequence operations.
In this short paper we have produced different kinds of upside down magic squares based on a palindromic day 11.02.2011. In this day appear only the algorisms 0, 1 and 2. Some of the magic squares are bimagic and some are palindromic. Magic…
In this short note we have given an equation based on the date 11.09.2001 and presented some magic squares. The magic squares presented are of order 3x3, 4x4, 5x5, 9x9, 16x16 and 25x25. While the magic square of higher order 9x9, 16x16 and…
The purpose of this paper is to give the flavor of the subject of self-similar tilings in a relatively elementary setting, and to provide a novel method for the construction of such polygonal tilings.
The super edge-magicness of graphs of equal order and size has been shown to be important since such graphs can be used as seeds to answer many questions related to (super) edge-magic labelings and other types of well studied labelings, as…
Using computational algebraic geometry techniques and Hilbert bases of polyhedral cones we derive explicit formulas and generating functions for the number of magic squares and magic cubes.
Discrete orthogonal matrices have several applications in information technology, such as in coding and cryptography. It is often challenging to generate discrete orthogonal matrices. A common approach widely in use is to discretize…
This paper proposes a simple technique of curve and surface construction with B-splines. Given a control polygon or a control mesh together with node ordinates corresponding to all control points, a rational curve or surface is obtained by…
In this paper, we give a constructive method for linear extensions of Zadeh's fuzzy orders. We also characterize Zadeh's fuzzy orders by their linear extensions.
In this short paper we show that with a small change of the common ruler and compass construction of the regular pentadecagon, we can produce more regular polygons
Magic-square constraints define Diophantine systems whose solutions, in several natural families, exhibit rigid periodic structure. We study this structure in an oracle setting, where a marked set of integers is given by black-box access…
Let $\Gamma$ be a group of order $n^2$ and $SMS_{\Gamma}(n)=(a_{i,j})_{n\times n}$ be an $n\times n$ array whose entries are all distinct elements of $\Gamma$. If there exists an element $\mu\in\Gamma$ such that for every row $i$, there…
A magic SET square is a 3 by 3 table of SET cards such that each row, column, diagonal, and anti-diagonal is a set. We allow the following transformations of the square: shuffling features, shuffling values within the features, rotations…
In this expository paper, we show how to use the Douglas-Rachford algorithm as a successful heuristic for finding magic squares. The Douglas-Rachford algorithm is an iterative projection method for solving feasibility problems. Although its…