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 Steiner Systems.
Orthogonal systems.
Orthogonal systems in vector spaces over finite fields.
Orthogonal systems of n-ary operations and codes
Ovals and non-ovoidal Laguerre planes.
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...
Overlapping Pfaffians.
and line-transitive linear spaces.
(3) as a symmetric (36, 15, 6)-design
Packing 10 or 11 unit squares in a square.
Packing graphs: The packing problem solved.
Packing of 180 equal circles on a sphere.
Packing unit squares in squares: A survey and new results.
Packings of pairs with a minimum known number of quadruples
Let be an -set. The problem of packing of pairs on with a minimum number of quadruples on is settled for and also for , , , , , where is any positive integer. In the other cases of methods have been presented for constructing the packings having a minimum known number of quadruples.
Packungen kongruenter Stäbchen mit konstanter Nachbarnzahl.
Pairs of disjoint -element subsets far from each other.
Parallel Class Intersection Matrices of Orthogonal Resolutions
This work was partially supported by the Bulgarian National Science Fund under Contract No MM 1405. Part of the results were announced at the Fifth International Workshop on Optimal Codes and Related Topics (OCRT), White Lagoon, June 2007, BulgariaParallel class intersection matrices (PCIMs) have been defined and used in [6], [14], [15] for the classification of resolvable designs with several parameter sets. Resolutions which have orthogonal resolutions (RORs) have been classified in [19] for designs...