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...

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

In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity. Orthogonality is also used with various meanings that...

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; he was...

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...

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...

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...

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

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...

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

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

of this form (λ = 2) are projective planes. The number of mutually orthogonal Latin squares of order N is at most N − 1. N − 1 exist if and only if there...

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...

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...

Cartesian coordinates, which are the signed distances from the point to three mutually perpendicular planes. More generally, n Cartesian coordinates specify the...

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...

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...

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

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...

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...

Retrieved 2023-09-27. "They can be colored as five sets of three mutually orthogonal planes" where the "fifteen planes divide the sphere into 120 Möbius...

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...

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

Newton's identities Ordered partition of a set Orthogonal design Complex orthogonal design Quaternion orthogonal design Packing problem Bin packing problem...

Problem 48 involved using a square with side 9 units. This square was cut into a 3x3 grid. The diagonal of the corner squares were used to make an irregular...

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...

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

distributed predictions, and not because mutually exclusive theories are true, which they cannot be, although two mutually exclusive theories can both be wrong...

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...