Sentence examples for square of order from inspiring English sources

A Latin square of order k is defined as a k × k square grid, the k2 cells of which are occupied by k distinct symbols of a set X = 1, 2,..., k, such that each symbol occurs once in each row and each column.

where the matrix B = X F ̄ L (23). is square of order 2L and obviously nonsingular.

An extra-high-order cube can then be solved in a relatively short time, which is merely proportional to the square of order.

An incomplete Latin square LS(n+a,a) is a Latin square of order n+a with a missing subsquare of order a.

If an incomplete latin square of order n has a hole of order m, then it is an easy observation that n≥2m.

A latin square of order n possessing a cyclic automorphism of order n is said to be diagonally cyclic because its entries occur in cyclic order down each broken diagonal.

When k − 1 mutually orthogonal Latin squares of order k exist, the set is complete.

An unsolved question is whether there can exist a complete set of mutually orthogonal Latin squares of order k if k is not a prime power.

There was also the long-standing conjecture of Euler, formulated in 1782, that there cannot exist mutually orthogonal Latin squares of order 4t + 2, for any integer t.

Two orthogonal Latin squares of order 4 are exhibited in Figure 2. A set of mutually orthogonal Latin squares is a set of Latin squares any two of which are orthogonal.

Indeed, the existence of an orthogonal array of k constraints, s levels, strength 2, and index unity is combinatorially equivalent to the existence of a set of k − 2 mutually orthogonal Latin squares of order s.