distinct. A set of Latin squares, all of the same order, all pairs of which are orthogonal is called a set of mutually orthogonal Latin squares. This concept...

An example is given below. Orthogonal arrays generalize, in a tabular form, the idea of mutually orthogonal Latin squares. These arrays have many connections...

plane of order n may be used to construct a set of n − 1 mutually orthogonal latin squares. Only the incidence relations are needed for this construction...

a right angle, whereas orthogonal is used in generalizations, such as orthogonal vectors or orthogonal curves. Orthogonality is also used with various...

by Leonhard Euler dated 1782 that there do not exist two mutually orthogonal latin squares of order 4 n + 2 {\displaystyle 4n+2} for every n {\displaystyle...

the diagonals) are said to be mutually orthogonal doubly diagonal Graeco-Latin squares. Odd squares: For the 3×3 odd square, since α, β, and γ are in arithmetic...

Leonhard Euler dated 1782 that for no n do there exist two mutually orthogonal Latin squares of order 4n + 2. Bose was born in Hoshangabad, India into...

block designs and their existence, and three on Latin squares and mutually orthogonal Latin squares. Other chapters cover resolvable block designs, finite...

by Leonhard Euler dated 1782 that there do not exist two mutually orthogonal latin squares of order 4n + 2 for any n. Shrikhande's specialties were combinatorics...

of Latin squares of the same order forms a set of mutually orthogonal Latin squares (MOLS) if every pair of Latin squares in the set are orthogonal. There...

1)(kn+1 − k)(kn+1 − k2)...(kn+1 − kn)/(k − 1). The number of mutually orthogonal Latin squares of order N is at most N − 1. N − 1 exist if and only if there...

factor, potential fractional designs to pursue are Latin squares, mutually orthogonal Latin squares, and Taguchi methods. Response surface methodology...

Gautham developed a novel Ab initio computational method using Mutually Orthogonal Latin squares (MOLS) - a technique employed in the area of experimental...

jl, retrieved 2019-11-15 OneWayANOVA Maple documentation Mutually orthogonal Latin squares Maple documentation "Probability or statistics - Does Mathematica...

of orthogonal Latin squares of order six. The 2-design with the indicated parameters is equivalent to the existence of five mutually orthogonal Latin squares...

origin and has (0, 0) as coordinates. The axes directions represent an orthogonal basis. The combination of origin and basis forms a coordinate frame called...

and conjugate transpose xH. An orthogonal matrix is a square matrix with real entries whose columns and rows are orthogonal unit vectors (that is, orthonormal...

In geometry, a quadratrix (from Latin quadrator 'squarer') is a curve having ordinates which are a measure of the area (or quadrature) of another curve...

pin. active Describes a piece that threatens a number of squares, or that has a number of squares available for its next move. It may also describe an aggressive...

relations corresponds to solving combinatorical problems involving Latin squares. Dagger commutative Frobenius algebras on qubits must be either special...

S-optimality This criterion maximizes a quantity measuring the mutual column orthogonality of X and the determinant of the information matrix. T-optimality...

Two vectors are orthogonal if ⟨u, v⟩ = 0. An orthonormal basis is a basis where all basis vectors have length 1 and are orthogonal to each other. Given...

standard deviation is equal to the square root of the difference between the average of the squares of the values and the square of the average value. See computational...

angles in triangles and squares. For example, in Circle Limit III every vertex belongs to three triangles and three squares. In the Euclidean plane,...

vice versa. As a space curve, a spherical conic is a quartic, though its orthogonal projections in three principal axes are planar conics. Like planar conics...

theorem since the basis vectors e1, e2, e3 are orthogonal unit vectors. This happens to be equal to the square root of the dot product, discussed below, of...

+\ell \mathbf {a_{3}} } because the lattice vectors need not be mutually orthogonal). By convention, negative integers are written with a bar, as in...

quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares" (PDF). Philosophical Magazine. 4th...

three given circles. For every set of four mutually tangent circles, there is a second set of four mutually tangent circles that are tangent at the same...

its side. The vertices of a regular icosahedron are those of three mutually orthogonal golden rectangles. Also, it is related to the Fibonacci sequence...