Showing papers on "Magic square published in 2014"
TL;DR: In this paper, a tensoring version of the Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities was constructed by tensoring conformal supermultiplets.
Abstract: By formulating $ \mathcal{N} $
= 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and single set of transformation rules, but with fields valued respectively in $ \mathbb{R},\mathbb{C},\mathbb{H},\mathbb{O} $
, it was recently shown that tensoring left and right multiplets yields a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was subsequently tied in with the more familiar $ \mathbb{R},\mathbb{C},\mathbb{H},\mathbb{O} $
description of spacetime to give a unified division-algebraic description of extended super Yang-Mills in D = 3, 4, 6, 10. Here, these constructions are brought together resulting in a magic pyramid of supergravities. The base of the pyramid in D = 3 is the known 4 × 4 magic square, while the higher levels are comprised of a 3 × 3 square in D = 4, a 2 × 2 square in D = 6 and Type II supergravity at the apex in D = 10. The corresponding U-duality groups are given by a new algebraic structure, the magic pyramid formula, which may be regarded as being defined over three division algebras, one for spacetime and each of the left/right Yang-Mills multiplets. We also construct a conformal magic pyramid by tensoring conformal supermultiplets in D = 3, 4, 6. The missing entry in D = 10 is suggestive of anexotic theory with G/H duality structure F
4(4)/Sp(3) × Sp(1).
67 citations
TL;DR: In this paper, the existence of regular sparse anti-magic squares with the second maximum density was investigated, and it was shown that there exists a regular SAMS ( n, n − 2 ) if and only if n ≥ 4.
11 citations
TL;DR: In this article, the split version of the Freudenthal-Tits magic square has been studied in the context of projective planes over 2-dimensional quadratic algebras, including Hermitian Veronese varieties, Segre varieties and embeddings of Hjelmslev planes of level 2 over the dual numbers.
10 citations
TL;DR: It is proved that a strongly symmetric self-orthogonal diagonal Latin square of order n exists if and only if n ≡ 0 ( mod 4 ) and n ≠ 4 .
9 citations
TL;DR: This study presents a range of effective selection hyper-heuristics mixing perturbative low-level heuristics for constructing the constrained version of magic squares, beating the best-known heuristic solution on average.
Abstract: A square matrix of distinct numbers in which every row, column and both diagonals have the same total is referred to as a magic square. Constructing a magic square of a given order is considered a difficult computational problem, particularly when additional constraints are imposed. Hyper-heuristics are emerging high-level search methodologies that explore the space of heuristics for solving a given problem. In this study, we present a range of effective selection hyper-heuristics mixing perturbative low-level heuristics for constructing the constrained version of magic squares. The results show that selection hyper-heuristics, even the non-learning ones deliver an outstanding performance, beating the best-known heuristic solution on average.
9 citations
01 Jan 2014
TL;DR: This paper proposes two algorithms for embedding and extraction of the watermark into the cover image based on magic square and ridgelet transform techniques that enabled the cover images to have the good invisibility and made them robust to the general image compression attacks such as JPEG, GIF.
Abstract: This paper proposes two algorithms for embedding and extraction of the watermark into the cover image based on magic square and ridgelet transform techniques. Spread-spectrum communication systems use the spread sequences that have good correlation properties. Magic square technique is used as a spread-spectrum technique to spread the watermark. Ridgelet transform is the next-generation wavelets as it is effective through line singularities characteristic. Ridgelet transform generates sparse image representation where the most significant coefficient represents the most energetic direction of an image with straight edges. The experiments indicated that these algorithms enabled the cover images to have the good invisibility and made them robust to the general image compression attacks such as JPEG, GIF.
8 citations
TL;DR: A unified treatment of the 2 × 2 analog of the Freudenthal-Tits magic square of Lie groups is given in this paper, providing an explicit representation in terms of matrix groups over composition algebras.
Abstract: A unified treatment of the 2 × 2 analog of the Freudenthal–Tits magic square of Lie groups is given, providing an explicit representation in terms of matrix groups over composition algebras.
7 citations
TL;DR: In this article, the authors describe a construction of regular classical magic squares that are nonsingular for all odd orders and a similar construction is given that produces regular classical Magic Squares that are singular for odd composite orders.
6 citations
TL;DR: In this paper, the authors present several effective ways for a magician to create a 4-by-4 magic square where the total and some of the entries are prescribed by the audience.
Abstract: We present several effective ways for a magician to create a 4-by-4 magic square where the total and some of the entries are prescribed by the audience.
4 citations
21 Oct 2014
TL;DR: This paper provides a necessary and sufficient condition for an even regular graph to be 2-factor-E-super magic decomposable and uses Petersen's theorem and magic squares to do so.
Abstract: An H-magic labeling in an H-decomposable graph G is a bijection f:V(G) U E(G) --> {1,2, … ,p+q} such that for every copy H in the decomposition, $\sum\limits_{v\in V(H)} f(v)+\sum\limits_{e\in E(H)} f(e)$ is constant. The function f is said to be H-E-super magic if f(E(G)) = {1,2, … ,q}. In this paper, we study some basic properties of m-factor-E-super magic labelingand we provide a necessary and sufficient condition for an even regular graph to be 2-factor-E-super magic decomposable. For this purpose, we use Petersen's theorem and magic squares.
4 citations
TL;DR: In this paper, homomorphisms and isomorphisms between groups of magic squares and real numbers are discussed, and the groups of groups of real numbers and magic squares are compared.
Abstract: Homomorphisms� and� isomorphisms� between� the� groups �of��� magic� squares ��and� real�� numbers� �are� discussed� in� this� paper.
TL;DR: In this article, a method for producing a variety of magic rectangles using -linear transformations was introduced, which adds significantly to the collection of known Magic Rectangles with non-coprime dimensions.
Abstract: We introduce a method for producing a variety of magic rectangles using -linear transformations. This adds significantly to the collection of known magic rectangles with non-coprime dimensions.
Journal Article•
TL;DR: A model for securing the SNMP communication with help of dual encapsulation is proposed and it is proposed how the communication from SNMP manager to SNMP agent or vice versa can be more securely done.
Abstract: We have proposed a model for securing the SNMP communication with help of dual encapsulation. Frist encapsulation is done with Magic square method and second with Ontology. SNMP has become a wide accepted protocol for network communication. In this paper it is proposed how the communication from SNMP manager to SNMP agent or vice versa can be more securely done. Keywords—SNMP; MIB; Magic Square; Ontology; Cryptography
TL;DR: Lee et al. as discussed by the authors proved that the classical regular magic square of odd order produced by the centroskew S -circulant matrix with the assignment a j = j − 1, j = 1, 2, ⋯, (n + 1 ) / 2 is always nonsingular.
Posted Content•
TL;DR: In this article, a short tribute to the guru of enumerative and algebraic combinatorics started out when one the authors(DZ) attended the Stanely@70 conference, that took place at the same time as the preliminary stage of the 2014 World Cup.
Abstract: This short tribute to the guru of Enumerative and Algebraic Combinatorics started out when one the authors(DZ) attended the Stanely@70 conference, that took place at the same time as the preliminary stage of the 2014 World Cup. It states a surprising application of an analog of Richard Stanley's famous theorem about the enumeration of magic squares to the enumeration of possible outcomes in a World Cup Group.
Patent•
05 Jun 2014
TL;DR: In this paper, a solution for 6×6=36 magic square where the numbers in each row, each column, and the forward and backward main diagonals are all add up to the same number is presented.
Abstract: The present invention relates to a solution for 6×6=36 magic square wherein the numbers in each row, each column, and the forward and backward main diagonals are all add up to the same number. Following is a method to complete the magic square having 36 grids including 6 rows and 6 columns: 1. filling numbers in the grids according to an initial drawing and checking constant sum of diagonals; and 2. arranging the remaining numbers in order and switching numbers in vertical symmetry of the rows, and numbers in horizontal symmetry of the columns from outer border in order to achieve the constant sum, and making the constant sum for inner lines.
TL;DR: In this article, the authors dealt with Latin squares, orthogonal Latin squares and mutually orthogonality of Latin squares with finite geometries, and proved that the conjecture was false.
Abstract: The present paper deals with Latin squares, orthogonal Latin squares, mutually Orthogonal Latin squares, close connections between Latin squares and finite geometries. Moreover the great mathematician Leonhard Euler introduced Latin squares in 1783 as a "nouveau espece de carres magiques", a new kind of magic squares. He also defined what he meant by orthogonal Latin squares, which led to a famous conjecture of his that went unsolved for over 100 years. In 1900, G. Tarry proved a particular case of the conjecture. It was shown in 1960 by Bose, Shrikhande, and Parker that, except for this one case, the conjecture was false.
TL;DR: The effect of various transformations on the eigenvalues and singular values of these special magic squares is considered in this paper, where numerical examples are presented and numerical values are obtained from simple formulas for the Eigenvalues of each of the 48 natural pandiagonal, regular, and bent-diagonal magic squares of order 4 and their reflections.
Posted Content•
TL;DR: In this article, a generalization of magic squares to finite projective space is studied. But the generalization is restricted to a special case where the sum along any $r$-flat is $0.
Abstract: This paper studies a generalization of magic squares to finite projective space $\mathbb{P}^n(q)$. We classify at all functions from $\mathbb{P}^n(q)$ into a finite field where the sum along any $r$-flat is $0$. In doing so we show connections to elementary number theory and the modular representation theory of $\operatorname{GL}(n,q)$.
Posted Content•
TL;DR: In this paper, the authors focus on a simple and easy method to construct doubly even magic squares, where the number of rows, columns, and diagonals is the same.
Abstract: Magic squares have been an enthralling topic in mathematics for centuries. They are formed by filling in all the cells of a square matrix with the numbers starting from one so that the sum of all rows, columns, and diagonals is the same. Magic squares have applications in entertainment, music and even cryptography. This paper focuses on a simple and easy method to construct doubly even magic squares.
TL;DR: In this article, the authors analyzed the impact of the Unruh effect on the quantum Magic Square game and found the values of acceleration parameter for which quantum strategy yields higher players' winning probability than classical strategy.
Abstract: We analyze the impact of the Unruh effect on the quantum Magic Square game. We find the values of acceleration parameter for which quantum strategy yields higher players' winning probability than classical strategy.
Posted Content•
TL;DR: In this paper, the authors seek for an answer on Smarandache type question: may one create the theory of Magic squares 4x4 in size without using properties of some concrete numerical sequences?
Abstract: In this paper we seek for an answer on Smarandache type question: may one create the theory of Magic squares 4x4 in size without using properties of some concrete numerical sequences? As a main result of this theoretical investigation we adduce the solution of the problem on decomposing the general algebraic formula of Magic squares 4x4 into two complete sets of structured and fourcomponent analytical formulae.
Posted Content•
TL;DR: The non-existence of magic square of squares in order three by investigating two new tools, the first is representing three perfect squares in arithmetic progression by two numbers and the second is realizing the impossibility of two similar equations for the same problem at the same time in different ways and the variables of one is relatively less than the other as discussed by the authors.
Abstract: This paper shows the non-existence of magic square of squares in order three by investigating two new tools, the first is representing three perfect squares in arithmetic progression by two numbers and the second is realizing the impossibility of two similar equations for the same problem at the same time in different ways and the variables of one is relatively less than the other.
Journal Article•
TL;DR: In this paper, the Loub Magic Squares are concretized via concrete examples, including the algebraic development of eigen values and magic sums of the square, the underlining sets under discuss of the squares, the rhotrix-matrix construction of square, introduction of the terminology, partitioning the squares and the proof of the generalized centre piece of square as and of the magic sum M(S) as where is the first term, is the common difference along the main column expressed as, and is the last term of the arithmetic sequence.
Abstract: Miscellany Properties of the Loub Magic Squares are concretized via examples. This work outlines via concrete examples that apt for generalizations the generalized (symbolized) and squares, the algebraic development of eigen values and magic sums of the square, the underlining sets under discuss of the squares, the rhotrix-matrix construction of the square, introduction of the terminology: Subelements of the squares, partitioning the squares, the proof of the generalized centre piece of the square as and of the magic sum M(S) as where is the first term, is the common difference along the main column expressed as , and is the last term of the arithmetic sequence, the proof of the square is magic when m is odd including the primes except when m is the oddest prime, and an example of the Cayley Table Magic Square. is the greater natural less than or equal to.
Posted Content•
TL;DR: In this paper, the authors investigated some properties of Smarandache sequences of the 2nd kind and demonstrated that these numbers are near prime numbers and showed that they can be computed in polynomial time.
Abstract: In this paper we investigate some properties of Smarandache sequences of the 2nd kind and demonstrate that these numbers are near prime numbers.
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TL;DR: In this paper, the main effects and at least some of the two-factor interactions are linear-trend-free (their estimates are unaffected if there is a straight line trend over time).
Abstract: An n by n magic square with entries 1 to n2 has all row and column sums equal. If n has k factors, then a factorial design with n2 runs and up to 2k factors can be obtained from this for which the main effects and at least some of the two-factor interactions are linear-trend-free (their estimates are unaffected if there is a straight line trend over time). An unconnected experimental design called a magic Latin square is a Latin square with additional blocking obtained from structured rows and columns.
Keywords:
factorial experiment;
gerechte designs;
Graeco-Latin square;
Latin square;
magic Latin square;
trend-free design
01 Jan 2014
TL;DR: In this article, the authors dealt with Latin squares, orthogonal Latin squares and mutually orthogonality of Latin squares with finite geometries, and proved that the conjecture was false.
Abstract: The present paper deals with Latin squares, orthogonal Latin squares, mutually Orthogonal Latin squares, close connections between Latin squares and finite geometries. Moreover the great mathematician Leonhard Euler introduced Latin squares in 1783 as a "nouveau espece de carres magiques", a new kind of magic squares. He also defined what he meant by orthogonal Latin squares, which led to a famous conjecture of his that went unsolved for over 100 years. In 1900, G. Tarry proved a particular case of the conjecture. It was shown in 1960 by Bose, Shrikhande, and Parker that, except for this one case, the conjecture was false.
13 Nov 2014
TL;DR: In this article, the authors introduce and study special types of magic squares of order six and present a parallelizable code based on the principles of genetic algorithms, which is called the magic constant.
Abstract: In this paper we introduce and study special types of magic squares of order six. We list some enumerations of these squares. We present a parallelizable code. This code is based on the principles of genetic algorithms. A magic square is a square matrix, where the sum of all entries in each row or column and both main diagonals yields the same number. This number is called the magic constant. A natural magic square of order n is a matrix of size n×n such that its entries consist of all integers from one to square of n. We define a new class of magic squares and present some listing of the counting carried out over two years.