Orthogonal arrays with parameters OA and 3-dimensional projective geometries.
Orthogonal colorings of graphs.
Orthogonal partitions and covering of graphs
Orthogonal permutation arrays and related structures
Orthogonal Resolutions and Latin Squares
Resolutions which are orthogonal to at least one other resolution (RORs) and sets of m mutually orthogonal resolutions (m-MORs) of 2-(v, k, λ) designs are considered. A dependence of the number of nonisomorphic RORs and m-MORs of multiple designs on the number of inequivalent sets of v/k − 1 mutually orthogonal latin squares (MOLS) of size m is obtained. ACM Computing Classification System (1998): G.2.1.∗ This work was partially supported by the Bulgarian National Science Fund under Contract No...
Orthogonal systems.
Orthogonal systems in vector spaces over finite fields.
Orthogonal systems of n-ary operations and codes
Overlapping latin subsquares and full products
We derive necessary and sufficient conditions for there to exist a latin square of order containing two subsquares of order and that intersect in a subsquare of order . We also solve the case of two disjoint subsquares. We use these results to show that: (a) A latin square of order cannot have more than subsquares of order , where . Indeed, the number of subsquares of order is bounded by a polynomial of degree at most in . (b) For all there exists a loop of order in which every...
Perfect factorisations of bipartite graphs and Latin squares without proper subrectangles.
Point Sets with Uniformity Properties and Orthogonal Hypercubes.
Power of a determinant with two physical applications.
Products of all elements in a loop and a framework for non-associative analogues of the Hall-Paige conjecture.
Quasigroup automorphisms and symmetric group characters
The automorphisms of a quasigroup or Latin square are permutations of the set of entries of the square, and thus belong to conjugacy classes in symmetric groups. These conjugacy classes may be recognized as being annihilated by symmetric group class functions that belong to a -ideal of the special -ring of symmetric group class functions.
Quasigroups and tactical systems.
Quasigroups arisen by right nuclear extension
The aim of this paper is to prove that a quasigroup with right unit is isomorphic to an -extension of a right nuclear normal subgroup by the factor quasigroup if and only if there exists a normalized left transversal to in such that the right translations by elements of commute with all right translations by elements of the subgroup . Moreover, a loop is isomorphic to an -extension of a right nuclear normal subgroup by a loop if and only if is middle-nuclear, and there exists...
Quintuplication of Room Squares
Random matrices, magic squares and matching polynomials.
Room designs and one-factorizations.
Self-orthogonal cyclic n-quasigroups.